In this fanfiction scenario, Percy's adaptation to Hogwarts would be a complex process. He'd first have to deal with the cultural shock of a new magical world. The Hogwarts houses would be different from the cabins at Camp Half - Blood. He'd need to figure out which house he belongs in. His skills with a sword might not be as useful as in his own world, but he could learn to use magic to enhance his combat abilities. Also, he'd have to make new friends and enemies, and learn how to navigate the social politics of Hogwarts while still holding on to his own identity as a demigod.
Well, if Percy goes to the past in fanfiction, he could encounter younger versions of the gods. Maybe he would befriend a young Zeus or Poseidon before they became so powerful and full of pride. He could also learn new and forgotten magic or fighting techniques that were lost over time.
Well, one possibility could be that Percy is framed for a crime he didn't commit. Maybe some powerful enemy uses magic or trickery to make it seem like he's violated a major demigod law. So, he's sent to a special prison for demigods. Inside, he has to deal with all sorts of other dangerous inmates, some of whom might be old enemies or just generally bad - tempered demigods. He'd probably try to find a way to prove his innocence and escape while also having to survive the various challenges within the prison.
In this fanfiction, perhaps Percy will make new friends at Goode who end up getting involved in his demigod world. There could be a plot where the school is in danger, and Percy has to use his powers and knowledge of the mythological world to protect it. Maybe he'll also have some interesting interactions with his teachers who suspect there's something different about him.
Perhaps in this fanfiction, Percy goes to Australia to find a hidden artifact that is crucial for the safety of the demigod world. Along the way, he teams up with local demigods (if there are any in the fan - created story). He would have to adapt to the Australian culture and environment, which is very different from what he's used to in the US. He might also face some new types of monsters that are native to Australia.
If Percy Jackson goes to Hogwarts in fanfiction, he would face a whole new set of challenges. The magical rules there are different from what he's used to. He'd likely be confused by spells at first. However, his combat skills would be really useful in Defense Against the Dark Arts classes. He could show the Hogwarts students some new fighting moves. And his demigod status would make him a bit of an outcast, but also someone very interesting. I think the teachers would be both intrigued and worried about him. He might also introduce some Greek mythology elements to Hogwarts, like the stories of the gods, which could be fascinating for the students there.
Well, he might meet some really tough Norse warriors. Maybe he'd get into some epic battles or challenges. He could also make new friends or enemies among the Norse gods and heroes there.
In a fanfiction where Percy Jackson goes to Forks, he might be really confused by the gloomy weather. He's used to more sunny and open places. He could meet the Cullens and there would be a clash of his demigod powers and their vampire abilities. Maybe he'd mistake them for some new kind of monster at first.
Well, he might meet Elsa and be really amazed by her ice powers. Since Percy is used to dealing with all kinds of magic in his own world, he could either help Elsa control her powers better or get into some trouble because of the different nature of the magic in Arendelle. Maybe he'd also team up with Anna to fight against some new threat that emerges in Arendelle.