Well, it could be about Percy having to adapt to his new divine family. Maybe he has to learn special water - related powers from Amphitrite that are different from what he already knows. He could also face challenges from other sea deities who are jealous of his new status.
Some of the traditional sea monsters like the Kraken could be antagonists. Since Percy is now in a more prominent position in the sea world as Amphitrite's adopted son, the Kraken might see him as a threat and try to attack him.
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.
Obviously, Percy Jackson himself. Since it's about him being the son of Amphitrite. Also, Amphitrite is likely to be a main character, as she is his mother. Other characters could include his friends from Camp Half - Blood, like Annabeth, who might have to deal with Percy's new identity and the changes it brings.
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.
One great fanfiction could be where Amphitrite takes Percy under her wing secretly. She could teach him some underwater magic that Poseidon doesn't know about. This would add an interesting layer to Percy's powers and his relationship with the underwater world.
Well, of course, Percy Jackson himself often makes an appearance. He could be a mentor figure to the adopted son, guiding him through the ropes of being a demigod. Annabeth is also common, perhaps helping the adopted son with her wisdom and knowledge of the mythological world.
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.
One unique storyline could be that Amphitrite has a premonition about Percy being the key to saving the entire oceanic realm from a dark force that not even the gods are fully aware of. So she starts guiding Percy in his dreams, which is a very different approach compared to the normal interactions in the Percy Jackson universe.
Well, one possible plot could be Percy struggling to adapt to his new 'mother' Khione. He might have to deal with her cold and often unfeeling nature. For example, she could be trying to train him in her own ways which are very different from what he's used to at Camp Half - Blood. Maybe she wants him to use his powers in a more aggressive way to serve her own purposes.