Perhaps Percy is sent to the mental hospital because his demigod abilities are misdiagnosed as schizophrenia. In the hospital, he befriends a girl who seems to have some strange powers of her own. Together, they discover that the hospital is being used as a cover for a monster lair, and they must fight to escape and warn the other demigods. The mental hospital setting adds an interesting layer of secrecy and confinement to the story.
One idea could be Percy starts having visions related to his demigod adventures in the mental hospital. The staff think it's part of his mental illness, but it's actually his connection to the Greek world trying to reach him. Maybe he meets other patients who are actually demigods in hiding too, and they have to figure out how to use their powers subtly without getting caught.
One idea could be that Percy starts seeing strange things in the mental hospital that are actually manifestations of Greek monsters from his past. Maybe he has to convince the doctors and other patients that he's not crazy while secretly fighting off these threats.
Another possibility is that Percy has suffered some sort of mental trauma from his battles. He's having nightmares and flashbacks, and his friends think the mental hospital can help him. But once inside, he realizes that there are dark forces at work in the hospital. He has to use his demigod powers subtly to protect himself and the other patients from these unseen threats.
One possible plot could be that Percy wakes up in the mental hospital with no memory of how he got there. He starts to notice strange things like the nurses and doctors seem to have an otherworldly aura. As he tries to regain his memory, he discovers that the hospital is a front for some sort of mythological experiment. He then teams up with other demigods who are also trapped there to escape and expose the truth.
It's possible that the main antagonist is a new mythological creature that has the ability to manipulate minds. It has lured Percy and other demigods to the mental hospital and is slowly driving them insane in order to feed off their fear and chaos energy.
In a fanfic, perhaps Percy and his friends accidentally stumble upon Medusa's lair while on a quest. But instead of immediately attacking, Medusa offers them a deal. She says she will give them a valuable clue to complete their quest if they help her get revenge on one of the minor gods who wronged her in the past. Percy and his friends then have to decide whether to trust Medusa or not.
One idea could be Percy discovers he has a new ability related to his gills that allows him to communicate with underwater creatures in a more profound way. Maybe he can understand their ancient languages and has to use this new skill to solve an underwater mystery that threatens both the sea world and the surface world.
A great plot for a 'Percy Jackson at School' fanfic would be Percy competing in a school - wide competition that is secretly a test by the gods. The tasks in the competition could be related to the skills he has learned in his demigod adventures, like sword - fighting or outsmarting a maze - like obstacle. Also, he could befriend a mortal student who starts to suspect there is something different about Percy and his friends, and Percy has to decide whether to reveal the truth or keep the mortal in the dark.
Perhaps being reborn as a child of Poseidon but with a twist. Instead of having the typical water - based powers, you have the power to communicate with sea creatures in a way that no one else can, like understanding their emotions and memories. Or being reborn as a demigod who has lost their memory but slowly regains it as they go on quests and face challenges, and each recovered memory reveals a crucial part of their past and a new power or ability.
Well, perhaps the succubus is sent by an enemy of the gods to disrupt Percy's relationships with his friends. She starts causing jealousy and strife among them by using her alluring powers. Or maybe she's tied to an ancient prophecy that Percy is involved in, and he has to either defeat her or convert her to the side of good to fulfill the prophecy.
One idea could be that Percy adopts a young demigod who has a very rare and powerful ability. Percy has to teach this new demigod how to control their powers while also protecting them from monsters who are after the new kid because of their potential. Another could be that the adopted demigod is from a different pantheon entirely, which causes some interesting cultural clashes and misunderstandings within the Camp Half - Blood environment.