It could be an ancient deity that was banished long ago. Maybe a primordial god or goddess who was considered too powerful or too dangerous for the other Olympians. For example, it could be Erebus, the god of darkness.
Well, some past gods might be amused. They'd see these modern interpretations of their stories and characters in the Percy Jackson fanfiction as a strange yet interesting new form of worship or at least attention. For example, Zeus might be a bit irked at some of the liberties taken with his character, but also secretly flattered that people are still so interested in him.
Most of the gods would be confused at first. Hera might see it as an opportunity to manipulate the situation for her own ends. She could try to use Percy's new connection to Ares to create more chaos or to further her own plans. Poseidon would be very conflicted. On one hand, he has a connection to Percy as his son, but now Percy has this new link to Ares which could put Poseidon in a difficult position among the other gods.
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.
Reacting to Percy Jackson fanfiction is quite an adventure. One aspect that can be really engaging is when the fanfiction delves deeper into the backstories of the minor characters. It gives them more depth and makes the whole universe feel more alive. Also, some fanfictions take a darker turn, exploring the consequences of the battles and the traumas the characters might have endured. It can be a bit different from the original series, but that's the beauty of fanfiction.
Apollo would probably love it. Since he is the god of poetry and creativity, he'd be intrigued by the different interpretations of himself in fanfiction. He might even get some new inspiration for his own creative works from it.
The teachers at the school would be completely clueless. They'd be trying to regain control of the assembly, but when faced with gods, their normal disciplinary methods would be useless. One teacher might try to be brave and tell the gods to leave, only to be turned into a small, squeaking mouse by Hecate as a warning. Meanwhile, Percy and his friends would be scrambling to fix the mess before things got even worse.
Well, it could be about Percy facing a new and powerful threat that even the Olympians can't handle easily. Maybe he discovers a hidden 13th Olympian who has been locked away for centuries and now is causing chaos.
Well, you could write a fanfiction where Percy loses his memory and has to rediscover his powers and his place among the demigods. Or perhaps a story about how the minor gods in the Percy Jackson universe form their own alliance because they feel overlooked by the Olympians. You could also create a fanfic that focuses on Annabeth's journey if she was separated from Percy and had to fend for herself in a dangerous situation.