The gods themselves could be the main antagonists. Since they cursed Percy, they might be trying to keep him in a state of misery or use him for their own purposes.
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.
The main antagonist could be one of the major gods who cursed Percy. For example, Zeus might be angry with Percy for some reason and decide to curse him. Zeus would then use his power to send all kinds of obstacles and enemies Percy's way. He could manipulate the weather to create storms that target Percy or send powerful monsters after him.
A possible plot for this fanfiction is that the curse makes Percy lose his memory bit by bit. He forgets his friends, his past adventures, and even his own identity. As he struggles to figure out what's wrong with him, he starts having strange visions that are both a clue to the curse and a danger in themselves. Maybe the gods who cursed him are trying to erase him from existence, and he has to rely on his instincts and the few remaining memories to fight back. He might meet new characters who are either trying to help him or are part of the gods' plan to keep him cursed.
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.
Percy would probably develop a greater sense of patience. Since he has all the time in the world, he could learn to wait for the right moment to act. This new - found patience could help him in his adventures and in his attempts to either break the curse or come to terms with his immortality. He might also study various things over the long years, becoming more knowledgeable and wise, which would also shape his character.
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.
The gods might show their protection in various ways. For example, they could directly intervene in battles Percy is in, using their divine powers to shield him from harm. They might also send him signs or omens to guide him away from danger.
Maybe Percy tries to break the curse. He could embark on a quest to find a powerful magical artifact or a long - forgotten spell that has the power to reverse his immortality. Along the way, he would face various challenges and meet interesting characters who either help or hinder his journey.