Some students might be in awe of him. His demigod status and the stories he could tell about fighting monsters would be really cool to them. Others might be a bit jealous, especially those who pride themselves on being pure - blood wizards and think their magic is superior. But then there would be those who would be friendly and curious, like the Weasley twins. They would probably want to team up with him to pull some epic pranks using his unique skills.
He could introduce some new combat styles to the Dueling Club. His experience in fighting monsters as a demigod would give him an edge. He might be a bit of an enigma to the Hogwarts professors too. They would be intrigued by his different kind of magic. And with his being betrayed, he could be a bit guarded at first, but gradually open up as he realizes that not everyone at Hogwarts is like those who betrayed him. He could also discover some hidden chambers or secrets in Hogwarts that have a connection to his demigod world, like a hidden place that has a link to the Greek gods.
In this fanfiction scenario, Percy's adaptation to Hogwarts would be a complex process. He'd first have to deal with the cultural shock of a new magical world. The Hogwarts houses would be different from the cabins at Camp Half - Blood. He'd need to figure out which house he belongs in. His skills with a sword might not be as useful as in his own world, but he could learn to use magic to enhance his combat abilities. Also, he'd have to make new friends and enemies, and learn how to navigate the social politics of Hogwarts while still holding on to his own identity as a demigod.
In such a fanfiction, perhaps Percy was betrayed by his family or friends in the Ministry. When he goes to Hogwarts, he might find solace in the old castle. He could reconnect with his siblings in a more understanding way, and learn new magic that helps him in his quest for revenge or self - discovery. He may also team up with some unexpected allies among the students and teachers.
If Percy Jackson goes to Hogwarts in fanfiction, he would face a whole new set of challenges. The magical rules there are different from what he's used to. He'd likely be confused by spells at first. However, his combat skills would be really useful in Defense Against the Dark Arts classes. He could show the Hogwarts students some new fighting moves. And his demigod status would make him a bit of an outcast, but also someone very interesting. I think the teachers would be both intrigued and worried about him. He might also introduce some Greek mythology elements to Hogwarts, like the stories of the gods, which could be fascinating for the students there.
His own family could have betrayed him in a sense. For example, if they put too much pressure on him to conform to their expectations and he felt suffocated. Feeling betrayed by their lack of understanding, he goes to Hogwarts to find a new sense of purpose and freedom away from the family drama.
If Percy Jackson goes to protect Hogwarts in fanfiction, it'd be an amazing crossover. Percy is used to facing all kinds of monsters, and at Hogwarts, he'd have to adapt to magic. He might form an alliance with some of the Hogwarts students. His speed and combat skills could help in protecting the school from any invaders, whether they be Death Eaters or other dark creatures.
He might initially be met with suspicion. The Hogwarts faculty are protective of their school and students. However, Percy could win them over with his courage. For example, if there was a dangerous situation, he would jump in to help, just like he did in his demigod adventures. Professors like McGonagall might be impressed by his loyalty and sense of justice.
Percy would likely be drawn to the Forbidden Forest. His adventurous spirit would lead him there. He might encounter magical creatures that are completely new to him. He could try to communicate with them using his own experiences with mythical beasts from his world. And when it comes to classes, he'd have a hard time with some like Potions as it has no equivalent in his demigod training, but he'd probably excel in Defense Against the Dark Arts as he's used to fighting all kinds of dangerous foes.
Yes, there are likely to be such fanfictions. Fanfiction writers often love to create crossovers, and combining the world of Percy Jackson with Hogwarts from Harry Potter is an interesting concept. Writers might come up with unique stories about how Percy Jackson could be involved in the founding of Hogwarts, perhaps using his demigod powers or knowledge from his own adventures.