Zeus is a possibility. As the king of the gods, he might see Percy's potential and adopt him to have an ally among the demigods. Another could be Poseidon, since Percy is already his son in the original story. It would be an interesting twist to have Poseidon formally adopt Percy in a more divine way.
Artemis might be an unexpected god to adopt Percy. Although she's a goddess of the hunt and chastity, she could see Percy's courage and his connection to nature (through his father Poseidon). She might take him in to train him in a different kind of combat, more focused on stealth and wilderness survival.
Well, it could be about Percy having a new life in the realm of the gods. Maybe he gets special powers and training from them. He might also face new enemies that are threats to the gods, and he has to use his newfound abilities to protect the divine world.
Maybe Percy unknowingly breaks some ancient and very strict laws of the Gods. For example, he might interfere with some sacred rituals or places that are off - limits to mortals, even demigods like him. In the fanfiction world, the Gods could be very unforgiving when it comes to such violations and decide to kill him as a result.
Probably Poseidon, as he is Percy's father and has a vested interest in his son's well - being. Zeus might also be protective in some cases, despite their past differences, as Percy is a hero who often saves the world which benefits Zeus's realm as well.
Well, without reading the specific fanfiction, it's hard to say exactly who Percy is. But generally, in a 'champion of the gods' scenario, Percy would be a central figure. He might be a hero with unique powers, like being able to control certain elements or having superhuman strength. He could be a character who has to face various challenges and tasks on behalf of the gods, kind of like a chosen one in a fantasy story.
It could be the Sage of Six Paths. Since he is a very powerful and almost god - like figure in the Naruto universe. He might have decided to take Naruto under his wing to further his growth.
Perhaps he has lost too many people close to him. If his friends, like Annabeth or Grover, were to die in a particularly tragic way, he could be so grief - stricken that he no longer wants to live in a world without them. He might think that death is the only way to escape the pain of their loss.
One possible plot could be Percy's struggle to survive in a new, unknown realm after being banished. He might have to find new allies and face new enemies.
One possible plot could be Percy struggling to control new, strange powers that come with the curse. Maybe he has to constantly battle against the dark impulses the curse brings out in him.
Zeus is often one of the main gods showing possessiveness. He sees Percy as a powerful asset or a potential threat, so he wants to keep Percy in check. Poseidon, as Percy's father, also shows possessiveness in a different way. He wants to protect Percy but also use his powers for his own purposes sometimes.
Ra, the sun god. Maybe the story is about Ra losing his power to make the sun rise, and Percy has to help him get it back. This could involve a journey through different realms, with Percy using his wits and Ra using his remaining divine knowledge to solve the mystery of what has happened to his power.