One idea could be Percy getting involved in the vampire - human drama in Forks. Maybe he discovers the secret of the Cullens and tries to find a way to co - exist with them, given his own experiences with different species in his own world.
Another plot could be Percy befriending Bella. He might introduce her to some of his demigod skills, like combat or survival skills, which could change the way she approaches the dangerous situations she often finds herself in. For example, when dealing with the Volturi or other threats in Forks.
One possible plot idea could be Percy encountering unique Alaskan mythical creatures that are different from what he's used to in other places. Maybe he discovers a tribe with a special connection to the gods that he has to help protect.
One idea could be Percy using his unique skills to solve a mystery at school, like a series of strange disappearances in the school basement. Another could be Percy facing a bully who turns out to be a monster in disguise. Or perhaps Percy starting a club at school to teach other students about ancient Greek mythology.
A plot could involve Percy being sent to Forks on a quest. He discovers that there's a powerful artifact hidden in the area that could cause chaos if it falls into the wrong hands. The vampires and werewolves in Forks are also after this artifact for their own reasons. Percy has to navigate the complex relationships between these two groups while also trying to keep his true identity as a demigod a secret. Along the way, he forms an unlikely friendship with Jacob, who helps him understand the ways of the werewolves.
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.
Perhaps a new, powerful demigod - vampire hybrid that Percy has to face. This hybrid could be causing trouble in Forks, and Percy has to stop it before it destroys the delicate balance between the vampires, werewolves and humans there.
One idea could be Percy trying to hide his demigod powers from his high school classmates while still using them to solve normal high school problems like bullying. Another could be Percy forming a secret club in school for other kids with special abilities. Or maybe Percy getting into a friendly rivalry with the school's star athlete in a non - combat - related sport like track and field.
One idea could be Percy arriving in Beacon Hills and being mistaken for a new supernatural threat. The local pack tries to figure out his powers and intentions. Another could be Percy teaming up with the pack to fight a common enemy that is drawn to the unique energy of Beacon Hills and Percy's own demigod powers. Maybe he also has to adjust to the high school life there while hiding his true identity from most of the students.
One possibility could be that Hermione uses her magic skills in Forks in unexpected ways. Maybe she helps the local people solve some strange problems that they can't figure out with normal means. For example, she could use a spell to find a lost item in the forest which is full of mystery in Forks.
Well, perhaps Harry could be a wizard - creature hybrid. In Forks, he might discover that the vampires there have a connection to the magical world he comes from. Maybe he uses his magic to help the Cullens with some sort of threat that normal vampire powers can't handle.
Well, it could be about Percy adjusting to the new environment in Forks. Maybe he has to deal with the gloomy weather and the small - town vibe that's so different from what he's used to. He might meet new friends or face some challenges specific to Forks.