In some cases, Jason himself could be the inadvertent instigator. Maybe he accidentally made Percy look bad in front of others, or he unknowingly took something that Percy considered very important. This could cause Percy to snap and beat him up.
It could be a third character. This character might manipulate Percy into thinking that Jason has done something wrong. So, technically, this third character is the instigator while Percy is just the one doing the physical act of beating up Jason.
Percy could be the instigator if he has a moment of rage or is misinformed. His impulsive nature might lead him to start the fight without fully understanding the situation.
It could be Percy himself if he's acting unjustly. Even though he's beating up Hercules, if his reasons are not noble, like if he's just being full of hubris, then he would be the antagonist.
Perhaps in the fanfiction, Percy is under some sort of dark influence. This could be from a new, unknown magical force. This influence makes him see Jason as a threat to his friends or himself, so he attacks Jason. Jason, on the other hand, is initially confused but then tries to fight back to defend himself while also trying to figure out what's wrong with Percy.
Obviously, Luke and Percy are the main characters. Luke is the one doing the beating, and Percy is the victim in this scenario.
Yes, there are quite a few. You can find some on popular fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Percy Jackson Beats Jason' and you'll get a list of relevant stories. Some might focus on a battle between them where Percy's skills and wits help him overcome Jason.
A powerful magician or sorcerer in the fanfiction world might betray them. Such a character could have their own agenda and see Percy, Jason and Nico as obstacles. They could use magic to create illusions and false evidence to make it seem like the three have committed wrongdoings.
A fan who really likes Sakura and wants to show her strength. They might be tired of seeing Sakura always in a support role and want to create a scenario where she takes the lead and shows her power by beating up Naruto.
It could be an old - fashioned village elder who has always been against Naruto. They might see him as a threat to the traditional way of life in the village and so start spreading rumors that lead to the villagers turning on him.
Obviously, Peter and Flash. It's possible that Peter is a hero - type character with a moral code that Flash has somehow violated. Flash could be a sidekick - turned - antagonist or just a regular character who has a conflict with Peter. Their personalities and the nature of their relationship in the original source material would be twisted in this fanfiction to lead to Peter beating up Flash.
It might be a test of strength. They could both be trying to prove themselves, either to their friends or to some higher power in the fanfiction world. They want to see who is truly the stronger hero.
It depends on the situation. If the girl was just acting out of anger without any real provocation, then she could be at fault. But if the boy had been harassing her or others, then he might be the one to blame.