There could be a group of interdimensional hunters in the new dimension. They hunt any beings that come from other dimensions because they believe it will disrupt the balance of their world. Percy becomes their target, and they use their advanced technology and knowledge of the dimension's terrain to try and capture him.
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.
A powerful dark wizard could be the main antagonist. This wizard has been ruling the other dimension with an iron fist and sees Peter as a threat to his power. He uses his dark magic to create all kinds of obstacles for Peter, from summoning monsters to casting spells that distort Peter's perception of reality.
A group of rogue ninja from the other dimension could also serve as the main antagonists. They might be jealous of Naruto's power from his original dimension and want to steal it for themselves. They could be led by a charismatic and devious leader who has a personal vendetta against Naruto for some reason, like he believes Naruto will disrupt their way of life in the dimension.
Well, perhaps Percy could find himself in a dimension where the laws of physics are completely different. He might have to learn new ways to use his powers. For example, if water behaves strangely there, like it's solid in some areas and gas in others, he'd have to adapt quickly.
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.
Perhaps a group of rogue time - traveling wizards. They come from a future in this dimension where the wizarding world has been destroyed, and they believe that changing the past (even if it means causing chaos) is the only way to save their future. They see Harry as a threat to their plans because he has a natural inclination to preserve the present order.
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.
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.
It could be a corrupted version of one of the Fairy Tail members from the other dimension. For example, an evil Natsu who uses his fire magic for destruction and domination. The real Natsu would have to face his own dark self and find a way to defeat him without losing his own identity.
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.