One possible plot could be Percy discovering his true parentage as the son of Amphitrite. He might struggle with his identity, as he has always known Poseidon as his father. This could lead to a journey of self - discovery where he has to learn about Amphitrite's powers and how they are now a part of him.
He would likely be very strong in water - based powers. For instance, he could have the ability to create powerful whirlpools or tsunamis with ease. He might also have a natural affinity for sea creatures, being able to communicate with them effortlessly. This would make him a great protector of the underwater world.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). There are often many talented writers who create stories about Percy being the son of Poseidon and Amphitrite. Another option is FanFiction.net. Just use the search function and type in relevant keywords to find some great reads.
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.
One common theme is family. Since Percy is the son of Poseidon and Amphitrite is Poseidon's wife, it often explores how Percy fits into this new family structure. Another theme is power. Percy already has his own powers from Poseidon, and Amphitrite being a goddess also has great power, so how their powers interact is often explored.
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.