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.
Perhaps Percy is in the hospital in fanfiction due to a strange curse. This curse could be slowly draining his life force or causing him to have really bad nightmares that are affecting his health. He might be waiting for a special prophecy or a visit from a powerful god or goddess who could break the curse. And while he's there, his friends from Camp Half - Blood might be trying to figure out a way to help him, and there could be some internal camp politics going on about how to deal with Percy's situation.
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.
In the 'Percy Jackson Disappears' fanfiction, perhaps Percy could be kidnapped by an unknown enemy. Maybe it's a new villain who has a vendetta against the demigods. This would lead to his friends, like Annabeth, going on a desperate search for him, facing many dangerous challenges along the way.
Well, in this fanfiction, Percy's immortality could lead to some really interesting character development. He may start to feel lonely as he realizes that he will outlive all of his friends. This could cause him to be more withdrawn at first. But then, as he interacts with the students at Westover Hall, he might find new meaning in his immortality. He could start to see it as a way to protect others not just for a short time, but for as long as he exists. He could also form deep and lasting friendships with those who accept him for who he is, regardless of his immortality.
In the fanfiction, Percy might face new challenges related to his demigod status. Maybe he has to deal with the aftermath of the war, like rebuilding Camp Half - Blood or helping new demigods adjust.
Well, he could end up in a situation where all his friends are incapacitated. For example, they are put under a powerful spell. Percy then has to be the lone warrior to fight against a group of evil demigods who are trying to take over Camp Half - Blood. He'd have to use his water - related powers in new and creative ways.
He might go on a solo adventure to discover more about his powers. He could encounter new mythical creatures that he hadn't seen around the camp. Maybe he'll meet some other demigods who are on the run or have their own secret quests.
Well, in this fanfiction, Percy controlling the Styx could lead to some really interesting plot developments. Since the Styx has such a significant role in Greek mythology, it could attract all kinds of mythical creatures and gods. Percy could find himself in the middle of a power struggle as different factions either try to use him or stop him. He might also use the Styx to travel to different realms or access hidden knowledge. And perhaps he would have to face the consequences of messing with such a powerful and sacred entity, like facing the wrath of Hades or other underworld deities.
He might become an even more powerful figure. The trident could enhance his abilities to control water and perhaps give him new powers related to the sea. He could use it to defend his friends and fight against stronger enemies.
In the 'Percy Jackson returns to Goode' fanfiction, it could be that Percy has to face some challenges related to his dual identity. On one hand, he is a normal student at Goode, on the other, he is a demigod. This could lead to some interesting situations where he has to balance between the two worlds. For example, he might have to hide his demigod skills during a school competition but still manage to win in a rather unexpected way. Also, there could be new characters introduced, perhaps a new demigod who also attends Goode and Percy has to team up with them to face a common threat.
In such a fanfiction, perhaps Percy could use his unique powers in new and unexpected ways. He might gain the support of some unexpected allies among the demigods or even some minor gods who are tired of the Olympian regime. This could lead to a large - scale battle where Percy's strategic thinking and combat skills are put to the ultimate test against the might of Olympus.