I think Percy would have a mixed reaction. On one hand, he might be flattered that people are so interested in his story that they write fanfic about it. On the other hand, if the fanfic distorts his character or the events he's been through in a way he doesn't like, he could get angry. For instance, if a fanfic makes him look cowardly when he knows he's been brave in real situations, he won't be happy. Also, if the fanfic has a lot of inaccuracies about the Greek mythology that he's so familiar with, that could also annoy him.
Percy might initially be curious. He'd start reading to see what these fan - made stories are all about. As he reads, he could find himself laughing at some of the wild ideas in the fanfic. But if it starts to cross a line, like making fun of his friends or changing the essence of his story too much, he'd likely stop reading and might even feel a bit violated that someone is messing with his story in that way.
He'd probably be shocked. Percy is used to living his own story, not reading someone else's take on it.
Some of them might be entertained. For example, Thor could see the similarities and differences between his world and Percy's world of gods and monsters and find it humorous. Others like Black Widow might analyze the characters' motives and strategies in the fanfic as she is used to understanding people's minds.
She might be shocked at some of the wild ideas in the fanfiction. Maybe she'd laugh at some of the more outlandish plot twists.
They might be very skeptical at first. After all, Percy's powers are based on Greek mythology which is quite different from their world.
Percy's reaction would be a mix of confusion and fascination. The world of Kratos is so foreign to him, with different rules and a much darker tone. However, he would also be drawn to the hero's journey that Kratos undertakes in the fanfiction, comparing it to his own journey as a demigod.
Ruby would be excited. She loves stories full of action and adventure, and Percy Jackson fanfiction would be right up her alley. Weiss might be a bit more reserved, but could still find aspects of it to enjoy, like the complex characters. Blake would be interested in the themes of the story, such as loyalty and friendship. Yang would be enthusiastic, especially about the fight scenes and the strong characters in the fanfiction.
Bruce Banner, when he's not in Hulk mode, would be really interested in the scientific aspects that might be hidden in the Percy Jackson fanfiction. Even though it's a world of magic, he could look for ways that the magic could be related to some kind of scientific principle. He might also be interested in how the characters control their powers, whether it's Percy with his water powers or the Avengers with their various abilities, and look for similarities in self - control and management of power.
Annabeth would be devastated. She and Percy have a deep connection. She might go into a state of shock at first, then be filled with a fierce determination to find out who was responsible and make them pay. She would probably also be racked with guilt, thinking she could have done something to prevent it.
He might be intrigued. After all, it's about a world he's somewhat connected to.
Percy could be a bit skeptical at first. He's been through a lot in his own world, and fanfiction might seem a bit strange to him. But as he reads more, he could get really into it. He might find himself rooting for the characters in the Red Pyramid fanfiction, especially if they remind him of his friends or himself in some way. For example, if there's a character who is an underdog but has great potential, just like Percy felt in his early days.
Athena, being the goddess of wisdom, might analyze the fanfiction. She could look at how the mortal writers understand the Greek mythology and use it to create new stories. She might be impressed by the intelligence and creativity of some of the fanfictions, or she might be critical of inaccuracies.