In this fanfiction, Percy could be exposed to different realms and dimensions that are part of Chaos' domain. He might meet some very strange and powerful creatures. Maybe he'll form alliances with them or learn from them to become an even greater hero. Also, his personality could change as he adapts to this new and wild environment under Chaos' care.
It's possible that some of Percy's old enemies, like Kronos' minions who somehow survived, might resurface in this fanfiction. They could be trying to stop Percy from achieving whatever goals Chaos has for him. Also, some of the gods might get involved. They could be curious about Percy's new situation, or they might be worried that Percy's new power under Chaos could be a threat to them. And then there could be some mysterious entities from the Chaos - related realms that we haven't heard of before in the original Percy Jackson stories.
Well, there could be new characters created specifically for this fanfiction. For instance, Chaos might have his own loyal servants or minions who interact with Percy. There could also be other heroes or demigods from different pantheons. They might come to Percy for help or to challenge him. And of course, Percy's mother, Sally. She might be worried about her son and try to reach out to him, even though he is now in the realm of Chaos. Her presence could add an emotional aspect to the story as Percy has to balance his new life with his love for his mother.
Maybe in the fanfiction, Percy is on the verge of death in a battle. Chaos, who has been observing Percy for a while, decides to save him and adopts him. Percy then embarks on a journey in Chaos's realm. He could be trained by powerful beings there and form new alliances. His relationships with his old friends from his previous life might be strained as they don't understand his new situation, but he also gains new friends who are loyal to him because of his connection to Chaos.
In this kind of fanfiction, Percy might gain new powers or a different status. Hera could train him in her own ways, perhaps teaching him more about the divine politics and how to navigate the complex relationships among the gods. He may also have access to resources and knowledge that he didn't have before, which could change his future adventures drastically.
If Percy Jackson were adopted by Artemis in fanfiction, he would likely be protected in a different way. Artemis is a powerful goddess. She could shield him from more threats than he's used to. His personality might also become more reserved like the hunters. He'd be part of a group that values chastity and loyalty to Artemis above all. This would put a strain on his relationships with some of his old friends who might not understand his new lifestyle.
Obviously, Percy Jackson himself is a main character. He's the focus as the adopted son of Chaos. Chaos would also be a major character, as Percy's adoptive father. There might be appearances from old friends like Annabeth. She could be worried about Percy in his new situation or even try to help him. Another character could be some of the primordial deities related to Chaos. They might be either allies or antagonists to Percy depending on the story.
One interesting plotline could be Percy's struggle to adapt to his new role as the adopted son of Chaos. He might have to deal with new powers that are both a blessing and a curse. For example, he could have the power to manipulate the very fabric of reality, but it comes with the risk of losing his humanity. Another plotline could be Percy facing off against old enemies from his past in the Percy Jackson series, but now with his newfound powers and status. It would be a test of his loyalty and how much he has changed.
His character would experience a major shift. Since Hera is a very powerful and complex goddess, Percy would be exposed to a whole new set of values and power dynamics. He might become more calculating, as he has to deal with Hera's often - convoluted plans. At the same time, he could gain a deeper understanding of the gods' world, which could make him more confident in his own abilities, but also more jaded about the true nature of the divine.
Maybe it could be due to some powerful magic or a unique prophecy. In many fanfictions, unexpected events like this are often triggered by such elements.