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 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.
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 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 Tartarus itself personified. As Percy is alone in this terrifying place, Tartarus could take on a form and directly oppose him. It would use all the horrors and challenges of the place to try and break Percy.
It could be an alternate version of Orochimaru. Maybe in this new dimension, he has achieved ultimate power and is using it to control the different ninja villages.
A powerful and corrupted duelist from a forgotten dimension could be the main antagonist. This duelist might have discovered a way to harness the power of the dimensional rifts for his own evil purposes. He could be using this power to create chaos and destruction across all the dimensions, and only the combined efforts of the heroes from different dimensions can stop him.
Another possibility is a group of outlaws or rebels in the banished world who don't trust Percy because he's from another place. They might think he's been sent to spy on them or take over. So they would constantly try to get rid of him. They could be very resourceful and know the ins and outs of the new world better than Percy, which would make them tough opponents.
It could be a new dark wizard that we haven't seen in the original series. This wizard might be jealous of Harry's fame and power and wants to eliminate him by making him disappear.