Perhaps a group of mortal students who have discovered some minor Greek magic items. They start using them to cause chaos at school and target Percy because they sense he's different. They don't understand the full power they're messing with and end up creating a lot of problems for Percy and his demigod friends.
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.
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.
Perhaps an old enemy from Greek mythology who has found a way to infiltrate the school in a modern form. This could be a minor god or a powerful monster. They want to get revenge on Percy and Nico for past defeats. They might be using the school's resources, like the science labs or the library, to create chaos or find a way to regain their full power.
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.
It could be a power - hungry Atlantean noble who wants to rule not just Atlantis but also the surface world. He sees Percy as a threat to his plans and tries to stop him at every turn.
A new and powerful demon that has emerged from the darkest corners of the underworld. This demon is bent on using Percy's connection to the overworld to break through the barriers between the two worlds and unleash chaos. It has powers that are different from what Percy has faced before, like the ability to manipulate the very essence of the underworld's environment.
A powerful Amazonian sorceress who has turned against her own kind and is now trying to use dark magic to take over the world. She could see Percy as an obstacle in her path and constantly try to defeat him.
Maybe it could be a demigod who has become obsessed with power through gaming. This demigod, let's say a child of Hades, discovers a way to use dark magic and combine it with gaming technology to try and rule over all the other demigods. He sees Percy as a major threat to his plans because Percy is so popular and has strong powers, so he constantly tries to undermine Percy at every turn.
The goddess Hera might also be a great antagonist. Since she has a history of interfering in the lives of demigods, she could be jealous or threatened by Percy's rebirth. She might try to stop him from reaching his full potential in his new life or cause trouble between him and his new allies.
A powerful demigod who has been corrupted by the idea of primordial power could be the main antagonist. They might believe that by allying with a primordial or obtaining their power, they can become greater than the gods. This demigod would then oppose Percy, who stands for the protection of the current order.