It could be a new teacher who is secretly a minor villain from the Percy Jackson universe. This teacher might be trying to undermine Percy's confidence and expose his demigod side to the mortal world. They could set up difficult situations for Percy in class, like impossible tests or false accusations of cheating. Also, they might try to turn Percy's friends against him by spreading rumors. The teacher could be working for a bigger bad guy in the background, but their main goal is to make Percy's high school life miserable.
A powerful sorcerer could be the main antagonist. He might be after Percy's powers or trying to use the school as a base to spread chaos. Maybe he wants to open a portal to the underworld right in the middle of the schoolyard.
Perhaps a new, powerful demigod - vampire hybrid that Percy has to face. This hybrid could be causing trouble in Forks, and Percy has to stop it before it destroys the delicate balance between the vampires, werewolves and humans there.
It could be a new demigod who has turned to the dark side. Jealous of Percy's popularity and Artemis' power, this demigod could try to create chaos in the high school and turn students against them.
The school principal could also be an interesting antagonist. Imagine if he or she has somehow been influenced by a dark power from the mythological world. They start implementing strict and unfair rules at the school that target the demigods specifically, and Percy has to figure out a way to break the influence without getting expelled.
A teacher at the high school could secretly be a minion of an evil god. They could be trying to undermine Percy and his friends by giving them unfair grades, getting them in trouble with the principal, and generally making their high school life miserable. This would be an interesting take as it's an unexpected source of conflict.
Maybe it's a corrupted version of one of the gods from Percy's world who has gained even more power in this new dimension. They could be trying to spread chaos and destruction, and Percy has to stop them. This antagonist would know Percy's weaknesses from their time in the original world, which would make the conflict more intense.
There could be an ancient and evil force that has infiltrated the demigod world. This force uses Percy as a scapegoat and arranges for him to be sent to prison. It wants to cause chaos and destruction within the demigod community. It manipulates the situation from the shadows, and Percy has to figure out its identity and motives while in prison in order to stop it.
Another option for the main antagonist in the fanfiction could be a jealous classmate. This classmate might be envious of Spider Man's popularity and powers. He or she could try to sabotage Spider Man at school, like spreading rumors about him or trying to get him in trouble with the principal. This would make Spider Man's school life even more difficult as he has to deal with both this classmate and any real threats to the city.
It could be another vampire who is jealous of Bella. Maybe this vampire has been at the school for a while and doesn't like the attention Bella is getting. So, they try to create problems for her, like spreading rumors about her or trying to get her into trouble with the school authorities.
It could be a dark wizard who has infiltrated Hogwarts under a disguise. Percy might be the one to first suspect this wizard's true identity.