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.
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 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.
There's a fanfic called 'Amphitrite's Influence on Percy'. This one focuses on how Amphitrite, being a powerful goddess, starts to influence Percy in different ways. It shows Percy growing in strength and wisdom under her guidance, and there are some really exciting adventures that he embarks on as a result.
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.
Well, it would make Percy's relationship with Poseidon extremely complicated. Since Amphitrite is Poseidon's wife in Greek mythology, if she's Percy's mother, it means Poseidon has a different kind of connection to Percy. Percy might feel more conflicted about his fatherly figure. He could be in a strange position where he has to navigate between the relationship with his mother and the traditional view of Poseidon as a powerful and somewhat distant god - father figure.
One possible storyline could be about their journey towards parenthood. Poseidon might be shown as being overprotective of Amphitrite during her pregnancy. He could use his powers to create a safe and comfortable environment for her in the underwater realm. For example, he could make a special grotto filled with magical sea plants that emit a soothing glow and provide healing properties to keep her and the unborn child healthy.
A possible fanfiction could explore how Amphitrite changes Poseidon. Before meeting her, he was perhaps more brash and impulsive. But with Amphitrite by his side, he becomes more patient and understanding. For example, when dealing with disputes among the sea creatures, he now listens more carefully and makes fairer decisions. Their love is a force that transforms them both for the better.
One great fanfiction idea could be Poseidon and Amphitrite's first meeting. In this story, Poseidon is out exploring the vast ocean when he comes across Amphitrite dancing among the waves. He is immediately smitten by her grace and beauty. The story could then follow his attempts to court her, facing various challenges along the way, like the jealousy of other sea nymphs.
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.