A prevalent theme is isolation. In many fanfictions, Percy feels alone because of his strange heritage. He doesn't quite fit in with the normal demigods. Also, the theme of destiny often comes up. He has a special destiny due to his parents that he is constantly striving to fulfill.
I've read a fanfiction where Percy is the son of Lupa and Chaos and it focuses on his relationships. 'Percy's Bonds' is the name. It shows how his different heritage affects his friendships and romances, and how he has to come to terms with who he really is in the context of his relationships.
In this fanfiction, there might be a lot of focus on Percy's relationship with the other wolves in Lupa's pack. He could learn their ways of survival, their hierarchy, and how to be a part of their community. This would be a great way to explore his adaptability and growth.
Lupa herself would be a major character. She's the one who has a special connection to Percy in this story. She could be guiding him, testing him, or having her own motives that are intertwined with Percy's journey.
The setting of the story might shift a bit. Instead of always being at Camp Half - Blood or on quests related to the Greek gods, Percy could be in the territory of the wolves. There could be new threats and challenges there, like rival wolf packs or ancient enemies of Lupa. And all these elements would make for an exciting and different take on the Percy Jackson universe.
In some fanfictions, Percy Jackson is indeed portrayed as the true son of Chaos. Writers often take creative liberties to explore new storylines and character developments. This idea can lead to very interesting and unique plot twists, such as Percy having powers beyond what we see in the original series.
One common theme is identity. Since Percy has two very different divine parents, he often struggles to figure out who he really is in fanfictions. Another theme is power. With the combined powers of Lupa and Poseidon, his power levels and how he uses them are often explored. Also, acceptance by his peers is a big theme as they may view his dual heritage as strange or overpowering.
One interesting plot could be Percy having to prove himself to Lupa's pack in a series of dangerous trials. Maybe he has to hunt a mythical beast that has been terrorizing the pack's territory.
The plot could center around Percy's transformation into the 'Son of Chaos'. He might have to face challenges that test his loyalty to his old friends at Camp Half - Blood while also adapting to his new role. He may also encounter new characters who are either allies or enemies in this new phase of his life. It might also involve a power struggle within the chaotic realm where he has to prove himself worthy.
One possibility for a Percy Jackson fanfiction centered around the Primordial Son of Chaos could be a story where Percy discovers a hidden prophecy related to this powerful being. Maybe he has to team up with some unlikely allies, like a group of minor gods who are also interested in the balance that the Primordial Son of Chaos might disrupt or uphold. This could lead to a series of adventures across different realms, including Tartarus, where they search for clues about the true nature of the Primordial Son of Chaos.