Well, in some fanfictions, Percy's experiences with monsters actually help him with the bullies. He has faced far scarier things than school bullies. So, he kind of sees them as just another nuisance. He may not even take their taunts seriously because he knows his own worth. He's a hero in the making, and these bullies are just small - time annoyances compared to the quests he's been on.
Percy could use his combat skills. If the bullies physically attack him, he can defend himself without seriously harming them. He's trained at Camp Half - Blood after all. Another way is to use his wits. For example, if they mock his dyslexia, he can come up with smart comebacks about how his different way of thinking gives him an advantage.
In Percy Jackson bullied fanfics, a common theme is the exploration of Percy's emotions. He might feel anger, sadness, or determination as a result of the bullying. Another theme is the contrast between the magical world he belongs to and the harsh reality of being bullied. It often shows how his demigod powers or his friends from the demigod world can help him face the bullies. Additionally, there can be a theme of transformation, where Percy grows from the experience of being bullied and becomes a more confident and capable character.
One possible scenario could be that Percy is bullied because of his dyslexia. The bullies might mock him for his reading difficulties, making him feel even more isolated. Another situation could be that his connection to the Greek gods is somehow revealed, and the bullies think he's crazy, so they pick on him. Or perhaps they're jealous of his skills in combat training that he got from Camp Half - Blood and target him out of envy.
One possibility could be that in the fanfiction, Percy is bullied at his new school in the mortal world because of his dyslexia and ADHD. Other demigods might also face similar situations. Maybe the bullies don't know their true identities but sense that they are different and pick on them.
One way could be for Percy to find a group of true friends who can support him. They can stand up to the bullies together. For example, if there are some nice classmates, Percy can join them during breaks and lunches, and the bullies might be less likely to target him when he's in a group.
Chiron, from Camp Half - Blood, might see it as a test of Percy's character. He would encourage Percy to handle it in a way that is both just and in line with his demigod nature. Chiron believes in teaching lessons through these difficult situations.
Percy often gets angry at first. He's not the type to just take it lying down. But he also feels a bit confused as to why Luke is being so mean. Sometimes he tries to stand up to Luke, but other times he just withdraws into himself, feeling sad and alone.
One common theme is Percy's struggle with his identity while being bullied. He might be bullied because of his ADHD or dyslexia, which are important parts of his character in the original series. Another theme could be his friends standing up for him, showing the power of friendship in the face of adversity.
The plot could involve Percy being bullied by a new group of monsters in disguise at Camp Half - Blood. These monsters, looking like normal campers, could be trying to weaken Percy before a big battle. Percy would start to doubt himself because of their constant taunts and pranks.