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.
There could be an ancient and evil force that has infiltrated the demigod world. This force uses Percy as a scapegoat and arranges for him to be sent to prison. It wants to cause chaos and destruction within the demigod community. It manipulates the situation from the shadows, and Percy has to figure out its identity and motives while in prison in order to stop it.
Percy might meet an old enemy who has somehow been resurrected or changed in the future. This enemy could be more powerful and have a new plan to take over the world or destroy the demigods. Or he could meet a group of time - traveling demigods from an even further future who are trying to fix something in Percy's future that has gone wrong.
Percy might run into Loki. Loki is known for his trickery. He could either befriend Percy for his own devious plans or try to deceive him. Percy, being used to dealing with tricky situations in his own world, would have to be on his guard against Loki's schemes.
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.
Some of the more traditional and rule - following demigod groups at Camp Half - Blood could be against him. They believe in following the established ways and Percy's rogue behavior goes against that. They might see him as a troublemaker and try to bring him back to the 'right' path.
In fanfiction, if Percy Jackson goes to highschool, he might face challenges like hiding his demigod powers from his classmates. He could also encounter new mythical creatures that are drawn to the school environment.
In a fanfiction where Percy Jackson goes to Azeroth, he could form alliances. Since he's used to being in a team in his own world, he'd likely team up with some of the heroes in Azeroth. For example, he could join forces with Thrall and help him in his quest for the Horde. His sword - fighting skills from Camp Half - Blood would come in handy in battles against the Burning Legion or other enemies.
The plot could center around Percy's struggle to fit in at college while still being a hero. He may find that the other students don't understand his need to disappear suddenly when there's a monster attack. He could also get involved in some sort of college - wide mystery that has roots in the ancient world. Like, strange symbols start appearing all over campus that only he can decipher because of his knowledge of Greek and Roman mythology. And he has to team up with some unlikely allies, like a nerdy professor who turns out to have a hidden knowledge of the demigod world, to solve the mystery and save the college from an impending doom.