One possible plot could be that Poseidon has to keep the female Percy hidden from the other gods because she's a girl and not the expected male hero. He might train her in secret on an isolated island, teaching her about her powers and the history of the gods.
Well, it could be about Percy and Poseidon having some sort of adventure together. Maybe they team up to face a new threat in the mythological world. Since it's a fanfic, the author might also explore their relationship in ways not shown in the original stories, like Poseidon teaching Percy some unique powers or skills.
Yes, there are likely some out there. You can start by looking on popular fanfic websites like Archive of Our Own. Search for the relevant tags such as 'Poseidon', 'female Percy' and 'raising'. However, the quality may vary greatly, so it's important to read the summaries and reviews if available.
In this type of fanfiction, a possible plot is that Poseidon raises Percy away from Camp Half - Blood to protect him from the prophecy. As Percy grows up, he becomes more in tune with his water powers. He could then have adventures in the ocean, like finding lost civilizations or facing off against sea monsters that Poseidon sends his way to test him.
One possible plot could be Percy discovers a hidden underwater grotto dedicated to Poseidon where he finds a magical lemon tree. The lemons have special powers that are only revealed when Percy and Poseidon interact near it. They could then go on an adventure to protect the grotto from a sea monster that wants to destroy it for its own gain.
The plot might involve Percy trying to bring peace between Poseidon and Athena. There could be some ancient feud between them that Percy is determined to end. He could start by finding common ground between the two deities in their respective domains, like the sea and wisdom. Along the way, he would face many obstacles, including other gods and goddesses who don't want the peace to happen.
One possibility could be a story where Percy and Artemis have to team up for a quest. Maybe there's a new threat to the world of the gods and their combined powers are needed. Percy's skills as a son of Poseidon in controlling water and Artemis's archery and connection with the moon could be crucial in defeating this new evil.
One possible plot could be Percy's struggle to balance his two powerful heritages. He might face challenges from both the forces of Chaos and the underwater world of Poseidon. For example, the denizens of the deep might be wary of his Chaos side, seeing it as a threat to their ordered underwater society. Meanwhile, the chaotic entities could try to pull him fully into their realm, away from his connection to Poseidon.
Well, it could be about Percy seeking advice from Poseidon on how to deal with a new and powerful enemy. Maybe he's facing a threat that only Poseidon's wisdom can help him overcome.
In a fanfiction, Percy could discover a new aspect of his powers that is related to Poseidon's domain but in a way that no one has ever seen before. For instance, he might be able to control not just water but also the weather patterns over the ocean. When Poseidon witnesses this, he is proud of Percy's growth and evolution as a demigod. He then takes Percy on a special journey to an underwater realm that is only accessible to a select few, to further train him.
In a 'Percy meets Poseidon' fanfic, Percy might seek advice from Poseidon. Maybe he's facing a new and powerful enemy in the demigod world, and Poseidon could offer some godly wisdom or a special weapon to help him. For example, Poseidon could give Percy the power to control a new aspect of the sea, like the ability to summon sea monsters that are loyal only to Percy.