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.
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.
A powerful sorcerer could be the main antagonist. He might be after Percy's powers or trying to use the school as a base to spread chaos. Maybe he wants to open a portal to the underworld right in the middle of the schoolyard.
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.
A powerful demigod who has been corrupted by the idea of primordial power could be the main antagonist. They might believe that by allying with a primordial or obtaining their power, they can become greater than the gods. This demigod would then oppose Percy, who stands for the protection of the current order.
A powerful Amazonian sorceress who has turned against her own kind and is now trying to use dark magic to take over the world. She could see Percy as an obstacle in her path and constantly try to defeat him.
Maybe a rogue demigod who blames Percy for something and wants to make his exile permanent. This demigod could have some dark powers or be in league with some evil forces. They would constantly try to thwart Percy's attempts to return or find a way to clear his name.
Maybe an ancient sea demon that has possessed a pirate captain. This possessed captain is now leading his crew to cause chaos everywhere. They are attacking other pirate ships and even some demigod - related places. Percy has to find a way to exorcise the demon from the captain and stop the crew's rampage. The demon is very cunning and uses the pirate's knowledge of the sea to its advantage.
The main antagonist could be Nyx. She is a powerful primordial goddess of the night, and Tartarus is her domain in a way. She might see Percy as an intruder and try to stop him from escaping or achieving his goals there.
It could also be a powerful sorceress who has her own motives for disrupting the demigod world. She might be seeking to gain control over the Olympian gods by using Percy as a pawn. She could use her magic to manipulate events and people around Percy, causing chaos and confusion.
Perhaps an ancient and dark deity who has been awakened due to some event related to Percy's exile. This deity wants to bring chaos to the world of gods and demigods, and Percy, even in exile, is the only one who can stop it. The deity would use all kinds of dark magic and minions to oppose Percy and his friends.