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.
There could be an ancient magical creature that has been awakened by some accident at Hogwarts. This creature sees Percy as a threat and becomes the main antagonist. Percy would then have to find a way to either defeat or pacify the creature.
It could be Voldemort if the story takes place during the time he was a threat. Naruto's arrival might disrupt his plans in some way, so he would see Naruto as an obstacle.
Maybe it could be a new character who is a combination of ninja and wizardry evils. This character could be jealous of Naruto's unique abilities that bridge the gap between two different worlds and wants to stop Naruto from uniting the ninja and wizarding communities against him. They could have powers that are a mix of dark magic and some dark ninja jutsus.
It could be a new dark wizard who has been lurking in the shadows. Maybe someone who was once a student at Hogwarts but turned to the dark side.
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.
Well, it could be that Percy has a hard time adjusting to the wizarding world at first. But then he meets a mentor figure who helps him understand his place in Hogwarts and he starts to thrive. He might even join the Quidditch team and become a star player.
Maybe a rogue ninja who has made a pact with a dark wizard in Hogwarts could be the main antagonist. This ninja - turned - villain has combined his ninja techniques with dark magic and is causing havoc in Hogwarts. Naruto would be sent to stop him, but he'd face a tough challenge as this antagonist knows both the ways of the ninja and the secrets of Hogwarts magic.
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.
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.