Can I propose an au where each of the Olympians imagined or fantasized about something while in Kronos’ stomach to keep them from going insane. Maybe they thought of what the sky might look like, maybe they thought of future children, maybe they even thought of getting bloody revenge on their father.
All this to say I want Poseidon to dream of Percy. I want him to imagine this sweet, sarcastic little boy who looks so much like him, who has no fear, and like the sea is unrestrained. I imagine Poseidon would grow to love this little boy who is living proof that Poseidon never becomes like Kronos (because Percy is never afraid of Poseidon in his dreams), that Poseidon has a future, and that there will be someone who will love Poseidon in the future (because Percy does love Poseidon and is concerned for him every time he sees him).
Also because Poseidon had the gift of prophecy maybe he is actually connecting to Percy or maybe he is just seeing the future. Imagine the angst though as time goes on and Poseidon sees all the scars and trauma Percy goes through unable to do anything or help in any way. Slowly coming to the realization that Percy MUST be real but that means that everything he is seeing is actually happening and that Percy can actually die.
What was once a source of comfort and hope quickly becomes a source of grief and despair as Poseidon realizes he will eventually have to watch his son die. Only he doesn’t because Zeus comes and they leave Kronos’ stomach and no matter how hard Poseidon tries he never sees Percy again, he never knows what happens to him.
I think it eats Poseidon up inside. I think when the gift of prophecy finally leaves him it is both a relief and another piece of Percy he has lost. I think Poseidon has son after son after son but none of them are quite right, none of them are Percy. I think he loves them because they hold pieces of the dream he clung to when he had nothing. I think he loves his immortal children in a way that someone clinging to something they cannot grasp can, because it is so much harder for him to lose these children compared to all his others (compared to Percy). Most of all I think he always remembers Percy and holds him special in his heart.
Eventually I think he starts to forget or manages to convince himself that Percy was always just a figment of his imagination. Something sweet to keep him sane when he was in his own personal hell. Only for him to meet a mortal woman, fall in love, and have a child. She names him Percy and he looks exactly like Poseidon, except softer and sweeter and something in Poseidon breaks. Because he knows how this story ends, suddenly all the scars and hurts he saw make so much more sense. Percy is the child the Great Prophecy talks about.
It hurts because the child Poseidon dreamed about, looked for, and wanted for so long is finally right in front of him, but there is a very real possibility he will die young. Percy will be hurt over and over again. Poseidon has seen it all happen, he knows what will happen, but there is nothing he can do. He cannot help, he is not even supposed to be here looking at his son right now. He can’t protect his son, he can’t save him and it hurts because he has loved him for so long. In the end all Poseidon can do is watch.