I'm not sure specifically as there could be many different takes on it. It might be a fanfiction where a character named Percy is disowned by his family or group. It could explore themes of isolation, self - discovery, and dealing with rejection.
Well, it could be that Percy has done something that goes against his family's values or rules. Maybe he's made a choice in his relationships or his actions that his family deems unacceptable, like befriending the wrong people or getting involved in a dangerous or taboo activity. And as a result, they disown him, leaving him to fend for himself and figure out his new place in the world.
You could try searching on popular fanfiction websites such as Archive of Our Own (AO3). They have a large collection of fanfictions and there's a good chance you'll find it there if it exists.
There are 'Percy Weasley disowned' fanfictions because his character has a lot of potential for drama. His estrangement from his family in the original story is a major plot point that fans like to explore further. Writers are interested in delving into Percy's psyche during this difficult time.
There could be a rival within the family. Someone who wants Percy out of the way, perhaps for inheritance reasons or because they're jealous of Percy's abilities or popularity. This rival could be the one who instigates the events that lead to Percy's disownment. And then there might be a mentor - like figure outside of the family who takes Percy in after he's disowned and helps him to grow and face his new situation.
It could also be an ancient prophecy that is misinterpreted. The Oracle might give a prophecy that the gods misunderstand as Percy being a threat. So, in an effort to prevent the prophecy from coming true in what they think is the wrong way, they disown him.
It could be that Percy's relationship with a certain god or goddess goes horribly wrong. Say he offends Aphrodite in a way that she convinces the other gods to disown him. Percy then has to struggle not only with the loss of his divine family but also with the isolation from the demigod community that follows such a disownment.
Well, the two main characters are Percy and Zoe. Percy, the son of Poseidon in the Percy Jackson universe, is known for his courage and loyalty. Zoe, who has been disowned by Poseidon, is now in a difficult situation. Their interactions, with Percy being the savior and Zoe the one being saved, will drive the plot of this fanfiction.
In this fanfiction, the plot could start with Zoe being cast out by Poseidon. Percy, being the hero he is, steps in. He first has to find Zoe as she might be in hiding or on the run. Then, he would have to fight off any pursuers. Along the way, they might develop a deeper bond as Percy helps Zoe come to terms with her new situation. Maybe they even team up to prove to Poseidon that Zoe is worthy.
Well, I'm not sure of the exact titles, but a good 'Percy Jackson disowned' fanfic would probably explore Percy's emotions deeply. It could show him feeling betrayed by his friends and the gods. Maybe it would have him going on a solo adventure to prove his worth. He might encounter new allies and enemies in the process. It could also be interesting if the fanfic explored how the other demigods reacted to his disownment, whether they supported him or not.