There's a spaceship, nearing the end of its journey. Everybody on board is in cryosleep. For some reason the wake-up system malfunctions, and the ship will fly on indefinitely. The people at the space port realise this, and try to wake someone up. Their last resort is finding someone on board who is telepathic, and wake this person up. They find one, but it turns out to be an unborn baby.
This is "Psyclops", a short story by Brian W. Aldiss; first published in New Worlds Science Fiction #49, July 1956, available at the Internet Archive (click here for download options); any of these covers look familiar?
The viewpoint character is an unborn telepathic baby on a spaceship. There is nobody else on board except his unborn twin sister and their mother. Nobody is in cryosleep, but the mother is not a telepath. The baby is receiving messages from his father, also a telepath:
Where are you?
I am on a world like Earth which is ninety light-years from Earth and getting farther from you even as we communicate together.
Why? How? Don't understand. So much is now beyond my understanding; before you came everything was peaceful and dim.
Lie quiet and don't fret, son. You're doing well; you take the points quickly, you'll reach Earth yet. You are traveling toward Earth in a spaceship which left Mirone, planet where I am, sixteen days ago.
The father is dying on the alien world they left:
We had wandered some way out from the ship when a group of natives burst out upon us.
People who live here. They are sub-human, blue-skinned and hairless—not pretty to look at.
I think you'd be better without one. Judy and I ran for the ship. We were nearly up to it when a rock caught me behind the knee—they were pitching rocks at us—and I went down. Judy never noticed until she was in the air-lock, and then the savages were on me. My leg was hurt; I couldn't even put up a fight.
The ship is going to miss Earth because the robot pilot does not have the correct data. The man instructs his unborn son on how to call for help:
Unfortunately, whereas spaceships get anywhere in time, thought has a definite limited range. Its span is as strictly governed as—well, as the size of a plant, for instance. When you are fifty light-years from Mirone, contact between us will abruptly cease.
Don't leave me. I shall be lonely!
I'll be lonely too—but not for long. But you, son, you are already halfway to Earth, or as near as I can estimate it, you are. As soon as contact between us ceases, you must call TRE.
Telepath Radial Earth. It's a general control and information center, permanently beamed for any sort of emergency. You can raise them. I can't.
They won't know me.
I'll give you their call pattern. They'll soon know you when you telemit. You can give them my pattern for identification if you like. You must explain what is happening.
Will they believe?
Are they real?
Of course. Tell TRE what the trouble is; they'll send out a fast ship to pick Judy and you up before you are out of range.
UPDATED in response to a comment from the OP.
In the one I remember the whole problem lies in comunicating with an unborn baby
You are in danger and I must help you.
Mmmmm. Must be mmmm. . . .
. . . If only there were a psychofetalist within light-years of here. . . . Well, keep trying. Wake up! You must wake up to survive!
who's in a womb experiencing a state of bliss 'Mmmm'.
First statement: I am I. I am everything. Everything, everywhere.
[. . . .]
Why am I having thoughts? Why am I not, as I was before, just mmmm?
Wake up! It's urgent!
No! Deny it! I am the universe. If you can speak to me you must be me, so I command you to be still. There must be only the soothing mmmm.
When the telepathic 'voice' intrudes, there is a brief conversation, but after a while the baby tires from it, and goes back to 'mmm',
You will—if nothing is done about it. But landfall will be delayed by thousands of years.
You are growing fainter. Strain too much. Must mmmm.
and there the story ends.
That was the end of the telepathic conversation but not the story. The end of the story:
Father! Wait, wait, look, see, I can move. I've just discovered I can turn, Father!
No answer now. Just a stream of silence. I have got to call TRE.
Plenty of time. Perhaps, if I turn first. . . . Easy. I'm only six months, he said. Maybe I could call more easily if I was outside, in the real universe. If I turn again,.
Now if I kick. . . .
Ah, easy now. Kick again. Good. Wonder if my legs are blue.
Kick. . . .