Is there any reference to Targaryens literally being "Blood of the Dragon"?

Question

From what I have read in the books and seen in the show, several Targaryens have either fathered or given birth to "deformed" children, many or all of which have had draconic features such as wings and tails.

Are there any references in any of the later books that I have not read that gives evidence that the Targaryens literally have dragon blood?

Answer 1

This is my own opinion supported by facts which formed it.

I'd say No, there is no evidence for it other than few curious things.

This Blood of the Dragon thing is not exclusive to Targaryens, it has existed since the day Valyrian freehold was established.

It is something we might call a National myth which Valyrians created to set themselves apart from rest of the world.

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We have to learn why did Valyrians need such a myth?

Civilization envy

Valyrians, despite their later successes, were in fact not the first people to adopt civilization or to found an empire of conquest. It was actually the Ghiscari who managed to do that.

AS WESTEROS RECOVERED from the Long Night, a new power was rising in Essos. The vast continent, stretching from the narrow sea to the fabled Jade Sea and faraway Ulthos, seems to be the place where civilization as we know it developed.

The first of these (not withstanding the dubious claims of Qarth, the YiTish legends of the Great Empire of the Dawn, and the difficulties of finding any truth in the tales of legendary Asshai) was rooted in Old Ghis: a city built upon slavery.
_{TWOIAF-The Rise of Valyria}

Ghiscari soon started expanding after formation of their city state and its fabled lockstep legions.

Old Ghis and its army proceeded to colonize its surroundings, then, pressing on, to subjugate its neighbors. Thus was the first empire born, and for centuries it reigned supreme.
_{TWOIAF-The Rise of Valyria}

In the meanwhile, Valyrians were limited to their peninsula, without any dragons or any civilization.

Daenerys had it rubbed in her face as well when she showed pride in her Valyrian roots in front of the Ghiscari.

Dany knew she would take more than a hundred, if she took any at all. "Remind your Good Master of who I am. Remind him that I am Daenerys Stormborn, Mother of Dragons, the Unburnt, trueborn queen of the Seven Kingdoms of Westeros. My blood is the blood of Aegon the Conqueror, and of old Valyria before him."

Yet her words did not move the plump perfumed slaver, even when rendered in his own ugly tongue. "Old Ghis ruled an empire when the Valyrians were still fucking sheep," he growled at the poor little scribe, "and we are the sons of the harpy."
_{ASOS-Daenerys II}

So as evident, Ghiscari at least viewed Valyrians with scorn due to the pride that theirs was an empire and civilization far older than Valyria's.

Valyria had to contest with Ghis first (Similar to Roman-Carthaginian wars in early days of our world) So how do you crush the pride your enemy had? You can't refute that they are indeed the first civilization and the first Empire. So what do you do? You create a myth that you were infact superhumans, descendants of dragons! Which gives your people pride in their own selves and scorn for your enemies.

The myth begins

Once the Valyrians had learned how to tame their dragons, they set forth to carve their own empire. Since they had dragons which no one else had, what better icon was there to form their national myth?

It was on the great peninsula across from Slaver’s Bay that those who brought an end to the empire of Old Ghis—though not to all of their ways—originated.

Sheltered there, amidst the great volcanic mountains known as the Fourteen Flames, were the Valyrians, who learned to tame dragons and make them the most fearsome weapon of war that the world ever saw.

The tales the Valyrians told of themselves claimed they were descended from dragons and were kin to the ones they now controlled.
_{TWOIAF-The Rise of Valyria}

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Criticism of the Myth

This is what is said about origin of Dragons:

The Valyrians themselves claimed that dragons sprang forth as the children of the Fourteen Flames, while in Qarth the tales state that there was once a second moon in the sky. One day this moon was scalded by the sun and cracked like an egg, and a million dragons poured forth.

In Asshai, the tales are many and confused, but certain texts—all impossibly ancient—claim that dragons first came from the Shadow, a place where all of our learning fails us. These Asshai’i histories say that a people so ancient they had no name first tamed dragons in the Shadow and brought them to Valyria, teaching the Valyrians their arts before departing from the annals.
_{TWOIAF-The Rise of Valyria}

So it is evident, that Dragons had existed long before Valyrians learned to tame them. If they were actually descended from dragons and all they needed was their blood to tame the dragons, Why didn't they do it sooner? Why didn't they do it when Ghis was expanding its Empire and Valyrians were a small isolated people?

The dragons were not even exclusive to the Valyrian peninsula either. They were found all over the world. If Dragons could give birth to humans, why is it there was no other such race any where? But if indeed we are to believe that Dragons did originate in Valyria and then migrated elsewhere, why is it that the Blood of the Dragon couldn't stop their migration until they learnt how to control them?

But there were dragons in Westeros, once, long before the Targaryens came, as our own legends and histories tell us.

If dragons did first spring from the Fourteen Flames, they must have been spread across much of the known world before they were tamed. And, in fact, there is evidence for this, as dragon bones have been found as far north as Ib, and even in the jungles of Sothoryos. But the Valyrians harnessed and subjugated them as no one else could.
_{TWOIAF-The Rise of Valyria}

The second part of the myth was the way they looked, which was used to emphasize that Valyrians were different from rest of the humans.

The great beauty of the Valyrians—with their hair of palest silver or gold and eyes in shades of purple not found amongst any other peoples of the world—is well-known, and often held up as proof that the Valyrians are not entirely of the same blood as other men.

Yet there are maesters who point out that, by careful breeding of animals, one can achieve a desirable result, and that populations in isolation can often show quite remarkable variations from what might be regarded as common.
_{TWOIAF-The Rise of Valyria}

Physical features do not necessarily mean that one race is not part of humanity but something else. We know that in Planetos, different races exist which can be correlated to White, Black, Brown, Asian people in our own world. Given the physical differences between all of them, there is no way to assert that one race maybe uber-human or inhuman.

Physical differences between actual dragon blood and Targaryen blood

We know from The Princess and the Queen and The Rogue Prince prequels that dragon blood:

1. Is hot.
2. Emits smoke
3. Is black

Stormcloud had been terribly wounded as he fled, arriving with the stubs of countless arrows embedded in his belly and a scorpion bolt through his neck. He died within the hour, hissing as the hot blood gushed black and smoking from his wounds.
_{The Princess and the Queen}

Also:

Dany could hear someone pounding after her. "Drogon," she screamed. "Drogon." His head turned. Smoke rose between his teeth. His blood was smoking too, where it dripped upon the ground. He beat his wings again, sending up a choking storm of scarlet sand. Dany stumbled into the hot red cloud, coughing. He snapped.

[....]The dragon gave one last hiss and stretched out flat upon his belly. Black blood was flowing from the wound where the spear had pierced him, smoking where it dripped onto the scorched sands. He is fire made flesh, she thought, and so am I.
_{ADWD-Daenerys IX}

Also:

Vhagar’s carcass plunged to the lake floor, the hot blood from the gaping wound in her neck bringing the water to a boil over her last resting place.
_{The Princess and the Queen}

Also:

Sunfyre’s scales still shone like beaten gold in the sunlight, but as he sprawled across the fused black Valyrian stone of the yard, it was plain to see that he was a broken thing, he who had been the most magnificent dragon ever to fly the skies of Westeros. The wing all but torn from his body by Meleys jutted from his body at an awkward angle, whilst fresh scars along his back still smoked and bled when he moved. Sunfyre was coiled in a ball when the queen and her party first beheld him. As he stirred and raised his head, huge wounds were visible along his neck, where another dragon had torn chunks from his flesh. On his belly were places where scabs had replaced scales, and where his right eye should have been was only an empty hole, crusted with black blood.
_{The Princess and the Queen}

Targaryen blood however shows none of these characteristics. So at least they don't have Dragon blood literally.

But it must be noted that GRRM has used Black blood to describe the outcome of duel between Beric Dondarrion and Hound as well so Black may in fact just be a figure of speech or highlighting the effect of light on the color of blood.

Are there any shards of truth in the myth?

But we have to note the curious attraction and bond between the Dragons and Valyrians.

This [Selective breeding and incest] may be a likelier answer to the mystery of the Valyrian origins although it does not explain the affinity with dragons that those with the blood of Valyria clearly had.
_{TWOIAF-The Rise of Valyria}

In any case, we do know that Valyrians used blood magic to bind to dragons so it maybe that this was the factor behind this strange affinity.

We also have to note that Targaryens are noted to feel heat less than normal humans. Examples are Daenerys Stormborn and Aegon V Targaryen but then again we know how sweaty Viserys III got in Dothraki plains.

Also as you have noted, Daenerys and other Targaryens have given birth to malformed children with dragon-like features.

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Conclusion

1. Valyrians needed some myth to make themselves appear superior to other men.
2. Valyrians existed prior to controlling dragons, most likely in humble circumstances.
3. There may be some truth in the myth which can't be explained but could be effect of the magic that ran Valyria.
4. We do not know for sure yet as GRRM hasn't yet explicitly confirmed or rejected it.

Answer 2

The other (excellent) answer argues that it is a form of Targaryen/Valyrian marketing.

However, it could also simply be a misnomer, due to connected facts that do appear to be true.

1. Dragons seem to like the Targaryens above all others. We haven't seen many dragons in the present to confirm this. But since dragons are independent creatures with a mind of their own, there should have been historical occurrences of non-Targaryens bonding with dragons, even if the Targaryens were to quickly dispose of this non-Targaryen anomaly once they found out.
2. This seems to be the case for all Targaryens, including their descendants. When speaking about inheritance, "blood" is a very common figure of speech. If a familial line all shares a common quality, it can colloquially be said to be "in their blood".

So if the dragons favor the Targaryens, and whatever makes the Targaryens this way (likely to be favored by the dragons) is passed down ("it's in their blood"), then it's not that far-fetched to start referring to the trait (which makes Targaryens favored by the dragons) as "the blood of the dragon".

Similarly, Jon Arryn said that the seed is strong, not the sperm or genes. Seed is a bit more figurative, but still widely accepted to be correct usage. Jon Arryn does not need to know human biology or genetics to be able to identify a recurring pattern in Baratheon hair.
Jon Arryn's explanation was "flawed" (not literally correct), but it was the best way for him to express his findings. The same can be true of "blood of the dragon". Maybe the people who coined the phrase did not know the true origins, but they observed a pattern nonetheless.

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As a real world analogy, "hair of the dog" does not always refer to literal hair (even if the origins of the saying did refer to dog hair).

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There is another analogy I can make about a (possible) misnomer in Game of Thrones: dragonglass.

Disclaimer:
This is a theory of mine. I'm rather convinced of it, and I feel that there is enough evidence to make it at least plausible, but feel free to disagree. I'm aware that this is not a proven truth.

Edit
As discussed in the comments below, dragonfire is not yet proven to kill White Walkers. This is unsure as well, so it belongs to the theory itself, not the evidence to support the theory.

There are three things that are known to kill a White Walker:

• Dragonfire (not normal fire)
• Valyrian steel (not normal steel)
• Obsidian (colloquially known as dragonglass)

Dragonfire is inherently magical, so it's efficacy is impossible to discuss. It is an axiom. Magic fire beats magic ice. (edit not proven to be true yet. But if it is true, then we still can't discuss it and should simply accept that it does)

Valyrian steel is rumored to have been forged using dragonfire. It stands to reason that this is essential to why it works against White Walkers. The magical property that gives dragonfire the ability to kill the White Walkers seems to have been carried over to the Valyrian steel that is forged in it.

Obsidian shares no connection to dragons.

At best, you can argue that obsidian (in real life) is created near volcanic activity; which is an environment that a dragon could survive in. However, this does not seem to be the case for Westeros (e.g. Dragonstone is a treasure trove of dragonglass, but has no hot environment)

However, we have seen how the Night's King was created (although we maybe did not see the full ritual). The Children of the Forest drove a shard of obsidian into a (living) human's chest.
This directly connects obsidian to White Walkers (as opposed to dragons).

I believe that obsidian works against White Walkers not because it has something to do with dragons, but because it is also the material that created the Night's King (and by extension the White Walkers).
Coincidentally enough, I could refer back to "hair of the dog".

But obsidian is still called "dragonglass". Likely, this is a misnomer that was caused by a common trait (killing White Walkers), while the reason for obsidian killing White Walkers is completely unrelated ("hair of the dog" as opposed to "magical fire beats magical ice").

People saw the common trait, and assumed that obsidian must therefore be connected to dragons in some way. It also looks like glass, and therefore the name "dragonglass" came into use.

There is a recurring pattern in "blood of the dragon" and "dragonglass": nomenclature can be based on subjective perception rather than factual correctness.