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.
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.
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.
In this fanfiction, perhaps there is a misunderstanding between Luke and Percy. Luke might think Percy has betrayed him in some way, like siding with the wrong people in the context of their fictional world, and thus resorts to violence by beating him up.
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.
Well, it could be that Hercules has done something to Percy's friends or family. For example, Hercules might have accidentally injured one of Percy's close friends during a heroic adventure. Percy, being very protective, then decides to take matters into his own hands and beats up Hercules. Also, there could be a power struggle between the two, with Percy feeling that Hercules is becoming too powerful and a threat to his own world or community.
One possible plot could be that they have to team up to stop an ancient evil that is rising. Each of them brings their own unique powers to the table. Percy with his control over water, Jason with his power over the wind and lightning, and Nico with his ability to manipulate the shadows. They journey to different realms to find the artifacts needed to defeat this evil.
Well, Percy has his water powers which are extremely versatile. He can control water in all forms, use it for defense and offense. For example, he can create huge waves to overpower enemies. Also, his connection to the sea is very deep and it gives him a constant source of power, which might make him stronger than Jason who mainly has wind and flight - related powers.
In some fanfictions, Jason might be jealous of Percy because Percy has a closer connection to certain characters. For example, if Percy has a special bond with Annabeth that Jason wishes he could have. Maybe Percy is more well - known among the demigods, and Jason, coming from a different camp, feels left out or envious of Percy's status.