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.
In fanfiction, Percy could be in the hospital because he was captured by an enemy and tortured. Now he's there being healed by the camp's healers or some advanced demigod medical technology. Another possibility is that he's having some sort of identity crisis related to his demigod status and it's causing him physical and mental stress, so he's in the hospital for both medical and psychological help.
His best friend Grover would surely visit him. Grover would bring some of Percy's favorite foods from Camp Half - Blood, like blue cookies. Annabeth would also be there. She'd probably be reading books on mythology, trying to find a way to help Percy get better faster.
Well, he might meet other characters who also claim to have had strange experiences. They could form a sort of alliance, thinking they are all in the same boat, not realizing Percy's experiences are real in the context of the Percy Jackson universe. They could plan an escape together, believing they are being wrongly held.
Perhaps a powerful monster in disguise as a doctor or staff member. They could be using the hospital's resources to create a portal to the underworld or something equally dangerous, and Percy has to stop them. They would be constantly trying to drive Percy crazy or keep him from interfering with their plans.
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.
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.
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.
No. Percy Jackson is an original fictional series. Although it uses Greek mythology as its base, it has created a completely new world, characters, and storylines. Fanfiction usually implies building upon an existing work in a more derivative way, often by fans rather than the original creator. 'Percy Jackson' was created by Rick Riordan as an original concept.
In Percy Jackson fanfiction, families can be depicted in various ways. Some might show Percy's family having new and unexpected adventures together. For example, his mom could discover a new magical ability that she uses to protect the family from an ancient threat. Another idea could be that Percy's half - brother Tyson becomes a key figure in protecting the family from monsters that target them specifically because of Percy's fame among the demigods.