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.
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.
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.
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.
It could be a jealous demigod. Maybe someone who has always been envious of Percy's popularity and power. This demigod could spread lies about Percy that lead to his disownment, making them the main antagonist.
One possible scenario could be Percy being disowned because of his powers being seen as too dangerous. Maybe the other demigods or even his own family in the fanfic fear what he can do and decide to cut ties.
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.
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.
One possible plotline could be Harry finding new and unexpected allies outside of the wizarding world he once knew. Maybe he discovers a hidden community of magical beings who are shunned by the mainstream wizarding society and they take him in.