Well, it could involve the family servants or guardians. They might be witnesses to Percy's supposed misdeeds or be part of the scheme to get him disowned. On the other side, there could be Percy's schoolmates or comrades from some sort of training or group activity. They could be divided in their support for Percy. Some might believe he's guilty and turn their backs on him, while others might stand by him and help him fight against the false accusations that led to his 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.
Grover could also be a main character. He might be at the scene when Percy gets drunk and try to use his nature - related powers to sober Percy up. Grover could also provide some comical relief with his reactions to Percy's drunken state, like his horrified expressions or his attempts to herd Percy like he would a wild animal.
Artemis could be a major character. As the goddess associated with the Hunt, she would have a huge role. She might initially be skeptical of Percy's ability to protect the Hunt but gradually come to trust him. Thalia, who is part of the Hunt, would also be important. She has her own history with Percy and could be a key ally in the protection efforts.
There could be other gods and goddesses. For example, Athena might be there to offer her wisdom to Percy as he navigates his new role. Poseidon, being Percy's father, could also play a part, maybe giving him advice on handling the power of a major god.
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.
There could be an old gardener who mentors Percy. The gardener might teach Percy all about the plants in the garden, their needs, and how to keep the garden thriving.
Annabeth could be a main character. She might be skeptical at first about Percy's new ability to control Styx, but then she uses her wisdom to help him understand the implications and possible uses of it. For example, she could research ancient texts to find out if there are any hidden dangers or benefits to Percy's control.
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.
I'm not sure specifically since I don't know the exact fanfiction, but it could be his friends who might be either involved in his hacking activities or completely unaware of them. Maybe there's a mentor - like figure who guides him in the world of hacking.
There could be his friends like Annabeth. She might be the one who first notices Percy's change and helps others to see him in a new light as well.
One character could be a time - keeper or a wizard who has the power to send Percy back in time. This character could be an old and wise figure, full of knowledge about the past and the ways of time travel. Another could be a historical figure that Percy meets in the past. For example, a famous warrior or a philosopher who becomes Percy's ally or mentor.