One interesting plot could be Percy having to face a new type of monster that is related to Ananke's powers. Maybe it has the ability to manipulate time or fate in some way, and Percy has to figure out how to defeat it using his own skills and the help of his friends.
A possible plot could be that Percy is thrown into an alternate dimension where Ananke's rule is absolute. In this world, the rules of the normal Percy Jackson universe are turned upside down. He has to find a way to return to his own world while also dealing with the strange and often dangerous aspects of this new dimension.
Well, obviously Percy Jackson is one of the main characters. He's the son of Ananke in this fanfiction, so he's at the center of the story. His friends like Annabeth Chase and Grover Underwood are likely to be important characters too. They would probably be there to support Percy in his adventures and help him deal with the challenges related to his connection to Ananke.
One interesting plot could be Percy having to face off against Medusa's other children in a battle of wits and strength. Maybe they are out to prove themselves as worthy as Percy, who has the fame of being Poseidon's son. Another could be Percy having to deal with the stigma of being 'Son of Medusa' in a world that fears her so much. He might have to constantly prove he's not a monster like his 'mother' is perceived.
In some fanfictions, there could be a plot where Percy is faced with a moral dilemma due to his connection to the 'Son of the Pit'. Maybe he has to decide between using a dark power within him to save his friends or resisting it and finding another way, which would show his growth and the struggle between his good nature and the darker aspects of his heritage.
One interesting plot could be Percy's struggle with his new identity as the son of death. He might have to deal with being feared by others in the demigod community. For example, he could face challenges when trying to form alliances as other demigods are superstitious about his parentage.
One interesting plot could be the adopted son discovering his own unique powers that are different from the typical demigod powers in the Percy Jackson world. Maybe he has a special connection to an ancient and forgotten god, which leads to all sorts of adventures as he tries to figure out what it means and how to control it.
One interesting plot could be Percy's adventures in the underwater realm as the son of Amphitrite. He might discover new sea creatures and magical underwater places. Another could be his interactions with other demigods from a different perspective, since his mother is Amphitrite.
One interesting plot could be Percy discovering new powers related to being the'son of void'. For example, he might be able to manipulate dark energy in ways that help him in battles against new and powerful enemies. Maybe he can create portals to the void to escape or surprise his foes.
Maybe there's a plot where Percy has to team up with other demigods who also have primordial roots. Together, they have to face a great evil that is threatening to destroy the balance between the primordial and Olympian worlds. They would have to use their combined powers and knowledge to save both worlds.
Perhaps there's a plot where Percy forms an alliance with a dragon. He has to earn the dragon's trust, and together they go on a quest. The dragon might be the key to unlocking some ancient mystery that has been hidden for centuries, and Percy's unique heritage as the 'son of a dragon' plays a crucial role in this journey.
Well, in some fanfictions, there might be a plot where Percy teams up with other demigods who are also related to Titans in some way. They could go on a quest to find a way to prevent a Titan - related catastrophe from happening. This would involve a lot of adventure, like exploring ancient Titan ruins and facing dangerous monsters along the way. They'd also have to deal with the distrust from other demigods who see their Titan heritage as a threat.