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.
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.
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.
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.
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.
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.
Another theme is family. Amphitrite is related to Percy through Poseidon. Fanfictions may explore how this family connection affects their relationship, whether it's a source of conflict or a way to bring them closer. It could involve Percy having to deal with Amphitrite as a sort of step - mother figure in some stories.
Well, it could be that in Percy fanfiction, Percy shows courage and a connection to the sea world. Amphitrite, being a sea goddess, would be drawn to these stories. For example, if Percy is shown protecting the sea or having a special bond with sea creatures, it would appeal to her. Also, the fanfictions might depict new and exciting aspects of the sea world that she would enjoy reading about.
I've heard of 'Percy and Amphitrite: An Unlikely Alliance'. It's a great read. In this fanfiction, Percy finds himself in a situation where he has to work closely with Amphitrite. The author does a wonderful job of creating tension and chemistry between them. It's full of action and some really cool plot twists.
The theme of loyalty is also common. They have to be loyal to their own kind while also developing feelings for each other. For example, Percy is loyal to his fellow demigods, and Amphitrite has her duties as a goddess. How they balance this loyalty with their new - found relationship is often explored in these fanfictions.