And it is said that in Beleriand there arose a king, who was of Númenórean race, and he was named Elendil, that is Elf-friend. And he took counsel with the Elves that remained in Middle-earth (and these abode then mostly in Beleriand); and he made a league with Gil-galad the Elf-king who was descended from Fëanor.
History of Middle-earth V The Lost Road and Other Writings Part 1: "The Fall of Númenor and the Lost Road" Chapter II "The Fall of Númenor" (iii) The second version of The Fall of Númenor §13
But that land where Lúthien had dwelt remained, and it was called Lindon. A gulf of the sea came through it, and a gap was made in the Mountains through which the River Lhun flowed out. But in the land that was north and south of the gulf the Elves remained, and Gil-galad son of Felagund son of Finrod was their king.
History of Middle-earth V The Lost Road and Other Writings Part 1: "The Fall of Númenor and the Lost Road" Chapter II "The Fall of Númenor" (iv) The further development of The Fall of Númenor
About this time it is recorded that Nargothrond was full-wrought, and Finrod's sons were gathered there to a feast and Galadriel came from Doriath and dwelt there a while. Now King Inglor Felagund had no wife, and Galadriel asked him why that was; but foresight came upon Felagund as she spoke, and he said: 'An oath I too shall swear, and must be free to fulfil it and go into darkness. Nor shall anything of all my realm endure that a son should inherit.'
But it is said that not until that hour had such cold thoughts ruled him; for indeed she whom he had loved was Amarië of the Vanyar, and she was not permitted to go with him into exile.
History of Middle-earth XI The War of the Jewels Part 1: "The Grey Annals" §108-109
Then in great sorrow Fingon took the lordship of the house of Fingolfin and the kingdom of the Noldor. [Late pencilled addition: But his young son (?Findor) [sic] Gilgalad he sent to the Havens]
History of Middle-earth XI The War of the Jewels Part 1: "The Grey Annals" §157
In an isolated note found within the genealogies, scribbled at great speed but nonetheless dated, August 1965, my father suggested that the best solution to the problem of Gil-galad's parentage was to find him in 'the son of Orodreth', who is here given the Quenya name of Artaresto, and continued:
Finrod left his wife in Valinor and had no children in exile. Angrod's son was Artaresto, who was beloved by Finrod and escaped when Angrod was slain [in the Battle of the Sudden Flame], and dwelt with Finrod. Finrod made him his 'steward' and he succeeded him in Nargothrond. His Sindarin name was Rodreth (altered to Orodreth because of his love of the mountains.... His children were Finduilas and Artanaro = Rodnor later called Gil-galad. (Their mother was a Sindarin lady of the North. She called her son Gil-galad.) Rodnor Gil-galad escaped [the sacking of Nargothrond] and eventually came to Sirion's Mouth and was King of the Noldor there.
History of Middle-earth XII The Peoples of Middle-earth Chapter 11: "The Shibboleth of Fëanor" The Parentage of Gil-galad
There can be no doubt that this [the 1965 note above] was my father's last word on the subject; but nothing of this late and radically altered conception ever touched the existing narratives, and it was obviously impossible to introduce it into the published Silmarillion. It would nonetheless have been very much better to have left Gil-galad's parentage obscure.
History of Middle-earth XII The Peoples of Middle-earth Chapter 11: "The Shibboleth of Fëanor" The Parentage of Gil-galad
Put as concisely as possible, Finrod (Felagund) was first given a son named Artanaro Rhodothir (so contradicting the story in the Grey Annals that he had no wife) the second King of Nargothrond, and father of Finduilas. Thus 'Orodreth' was now moved down a generation, becoming Finrod's son rather than his brother. In the next stage my father (recalling, apparently, the story in the Grey Annals) noted that Finrod 'had no child (he left his wife in Aman)', and moved Artanaro Rhodothir to become, still in the same generation, the son of Finrod's brother Angrod (who with Aegnor held the heights of Dorthonion and was slain in the Battle of Sudden Flame).
History of Middle-earth XII The Peoples of Middle-earth Chapter 11: "The Shibboleth of Fëanor" The Parentage of Gil-galad
Much closer analysis of the admittedly extremely complex material than I had made twenty years ago makes it clear that Gil-galad as the son of Fingon was an ephemeral idea.
History of Middle-earth XII The Peoples of Middle-earth Chapter 11: "The Shibboleth of Fëanor" The Parentage of Gil-galad