One possible reason for Percy being kicked out in fanfiction could be that he was wrongly accused of stealing a powerful artifact from the camp. Maybe someone framed him to get him out of the way. As for what happens next, he could go on a journey to clear his name, finding allies outside the camp who believe in his innocence.
Perhaps he's kicked out because he's discovered to have a new, unknown power that the camp leaders fear. In the fanfiction, after being kicked out, he might meet an old enemy who, surprisingly, offers to help him understand and control this power. They form an uneasy alliance, with Percy constantly on guard but also seeing an opportunity to learn more about himself.
One reason could be if he was wrongly accused of stealing something important from the camp. Maybe a powerful magical item goes missing and Percy is the prime suspect because of his past issues with authority. Another reason might be if he accidentally endangers the camp in some way during a mission or training exercise. For example, if he unknowingly leads some dangerous monsters back to the camp.
A plot could be that Percy accidentally breaks an ancient and sacred rule of the camp while trying to save a fellow camper. As a result, he's kicked out. He then decides to seek refuge with his mortal family, but soon realizes that monsters are targeting them too because of his connection. So he has to protect his family while also finding a way to get back into the good graces of the camp.
Percy could also be very sad. He has so many memories and relationships at the camp. He might go into a state of depression for a while, not knowing where to go or what to do next. But then, he would probably start to think about how to get back in or how to make things right. He might start looking for evidence to clear his name if he was wrongly accused. He could also look for new allies outside of the camp who could help him in his situation.
Perhaps Percy was kicked out because of a prophecy that the camp elders misinterpreted. They thought that Percy's presence would bring great danger to the camp, so they made the hasty decision to expel him. It could also be that there was some sort of political intrigue within the camp. Some powerful figures at the camp might have seen Percy as a threat to their power and influence, and so they fabricated reasons to get him kicked out.
He might be really angry at first. He's given so much to the camp, and being kicked out like that without a proper explanation would make him furious. He could storm off, vowing to find out the truth and clear his name.
One idea could be a story about Percy's sister who was hidden away and discovers her true identity when she arrives at Camp Half - Blood. Another could be a time - travel fanfic where Percy goes back to the early days of the camp and has to deal with different versions of the gods. Or perhaps a story where Percy and his friends have to face a new, unknown monster that is immune to water, which really challenges Percy's powers.
One idea could be the children of the original demigods going on a quest to find a new, powerful artifact that's been lost. For example, a magical shield that once belonged to a forgotten hero. Another plot could involve them facing a new type of monster that's a combination of different mythological beasts, like a chimera with the powers of a manticore. They might also have to deal with internal camp politics as the new generation has different ideas about how to run Camp Half - Blood compared to their parents.
He could go on a quest to find a long - lost artifact that was stolen from the camp. Maybe it's a powerful weapon that once belonged to one of the gods. With his leadership skills and the help of his friends, he would face many challenges along the way.
One idea could be Percy having to face a new type of monster that is native to the area around Camp Jupiter. For example, a giant mechanical beast left over from ancient Roman battles. Another could be Percy forming an unlikely alliance with a Roman demigod who initially dislikes him because he's from Camp Half - Blood. Maybe they have to work together to solve a mystery within the camp that threatens both camps.
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.