Maybe it's a way to atone for something. Apollo might have done something in the past that affected Percy or his friends negatively, and by taking care of Percy, he is trying to make up for it. Or perhaps there is a prophecy that involves both of them, and Apollo taking care of Percy is part of fulfilling that prophecy.
He might be so immersed in his own real (in - story) life that fan - made stories seem unimportant. He has gods to deal with, monsters to fight, and friends to protect. Fanfiction is something created by fans outside of his own reality, so he has no reason to care.
In fanfiction, it could mean that Apollo uses his godly powers to protect Percy. Maybe he heals Percy when he's injured during his quests, as Apollo is the god of healing.
Percy would probably be angry at first. He has a strong sense of justice and being kidnapped against his will would make him fight back. He might immediately try to use his water powers to break free or at least create a distraction.
Well, if Percy is raised by Apollo, he could be trained in the arts of prophecy as well. This would give him an edge in anticipating future threats. Maybe he would be more in tune with the sun's power, and could use it to boost his strength during battles, much like how Percy already uses water powers but with a solar twist.
Percy would likely become more confident in his abilities. With Apollo's guidance, he'd expand his skill set and this would boost his self - assurance. He might also become more artistic or musical, influenced by Apollo's domains.
Percy would likely become more confident in his abilities. Apollo's influence would make him more outgoing and perhaps a bit more self - assured. He'd also probably have a greater appreciation for beauty and the finer things in life.
In some fanfictions, Percy's lack of care could be due to a change in his personality after a major event. For example, if he's been betrayed by someone close to him. He might feel that the world of demigods is not what he thought it was. So, he starts to distance himself and act as if he doesn't care about the things that used to matter to him, like protecting Camp Half - Blood or going on quests. This can add an interesting twist to the fanfiction's plot.
The plot could be centered around Percy's identity crisis. Since he's raised by Apollo, he might struggle with whether he should follow Apollo's more flamboyant and carefree ways or stay true to his own nature. He could be exposed to Apollo's many lovers and children, which would make him question his place in this complex family. Additionally, his relationship with other demigods would change. He might be seen as an outcast by some who are loyal to Poseidon, while others might be jealous of his connection to Apollo. This would lead to various adventures where he has to prove himself not just as a son of Poseidon but as someone with a unique upbringing under Apollo.
In this fanfiction, Percy's identity could be somewhat transformed. He may take on some of Apollo's traits. Maybe he becomes more confident in his appearance and charm, like Apollo. His combat style could also change. Instead of just relying on his swordsmanship and water powers, he could incorporate Apollo's archery skills. He would have to learn how to make and use arrows, and this new skill would make him a more versatile fighter. His relationship with other characters would shift too. Some might be jealous of his new connection with Apollo, while others would be curious about how he has changed.
Percy's character would likely become more versatile. He'd start to incorporate Apollo's traits like confidence and a love for the arts. His power set might expand to include things like healing, which is associated with Apollo. He'd also become more in tune with the sun and light, which could change his overall perspective on things.