In some fanfictions, it could be that Percy has new, uncontrollable powers that the camp doesn't understand. They see him as a threat and banish him. For example, if he starts to show signs of a power that was once associated with an enemy of the camp. It's also possible that Percy's loyalty is questioned. If he befriends someone from an opposing group, the camp might think he has turned against them and banish him.
In some fanfictions, Percy is heartbroken. He has considered the camp his home for so long, and being banished makes him feel lost and betrayed. He might go into a period of self - doubt, wondering if he really is as bad as they say.
It could be Ares. He is often portrayed as a violent and unpredictable god. Percy might banish him if he goes too far in causing wars and chaos among mortals. His banishment would have a huge impact on the battlefields of the mortal world.
One possible reason could be that he feels misunderstood. In the camp, everyone has high expectations of him as a son of Poseidon. If he makes a small mistake, it might be blown out of proportion. For example, if he accidentally causes a small flood during a training session, instead of being understood as still learning control over his powers, he could be harshly criticized. Another reason might be that he's tired of the constant danger at the camp. Every day there seems to be a new threat looming, whether it's a monster attack or some sort of internal camp conflict. He might just want to get away and have some peace for a while.
He could be angry. Percy has always been loyal to the camp, and being exiled unjustly would make him furious. He might vow to prove his innocence and show the camp they made a big mistake.
In some fanfictions, he might be exiled because of false accusations. Maybe someone frames him for a crime he didn't commit, like stealing a powerful artifact from the camp's vault. The camp leaders, believing the false evidence, have no choice but to exile him.
Conflict is a very common theme as well. There are often conflicts between Percy and the new characters he meets, either because of misunderstandings or because they have different goals. And there's also the overarching conflict of Percy trying to find a way back home or to reverse his banishment. This conflict drives the plot forward and keeps the story exciting.
Another option could be Wattpad. Although it has a wide range of content, including many fanfictions. You can search for the specific 'Percy Jackson Banished' fanfiction there. Just be aware that since it has a lot of different types of stories, it might take a bit more effort to find exactly what you're looking for compared to more specialized fanfiction platforms.
One possible plot could be that in a world where the gods of Percy Jackson and the Avengers co - exist, Percy is somehow tricked or forced to banish the Avengers. Maybe there's a power struggle among the gods and they see the Avengers as a threat to their power, so they use Percy, who has a strong connection to the divine world, to get rid of them. Percy might be conflicted as he may admire the Avengers' heroism but has to follow the gods' orders.
In some fanfictions, Percy might be banished because he goes against the traditional ways of the demigod society too much. For example, if he tries to form an alliance with a group that the other demigods consider enemies. His actions could be seen as a threat to the stability of their world, so they banish him to keep the peace.