For the female Percy Jackson, you can develop her character by showing her growth in understanding and using her powers. Since she has a connection to Poseidon, she could start off a bit unsure but as the story progresses, become more confident. As for the 'lemon' aspect, if there's a love interest, it can show her vulnerability and a different side of her. For Poseidon, show his fatherly side towards her, his pride or disappointment in her actions which can shape her character development as well.
In this fanfiction, the plot could center around a prophecy that involves the female Percy Jackson and Poseidon directly. She has to prove herself worthy of her father's legacy while also dealing with her own feelings for someone. The 'lemon' aspect could come in when she has some private moments with this person, perhaps on a secluded beach or in an underwater grotto, where they share some sweet and somewhat steamy exchanges.
One possible plotline could be Percy facing a new and extremely powerful sea monster that Poseidon can't directly interfere with, but through their unique father - son bond, Poseidon gives Percy hidden powers that help him in the fight. Another could be Percy exploring an ancient underwater kingdom that Poseidon has long kept secret, and there are many challenges and revelations along the way.
Obviously, Percy Jackson and Poseidon are the main characters. Percy, as the demigod son of Poseidon, has his own set of powers and a complex personality. He's brave and often impulsive. Poseidon, on the other hand, is a powerful god of the sea with his own motives and a sense of fatherly love towards Percy, which is often explored in these fanfictions.
The unique part is the new perspective it brings. Since Poseidon is usually male in the original series, having a female Poseidon changes the dynamics. For example, in some fanfictions, the female Poseidon might have a different approach to ruling the sea or interacting with other gods.
One interesting Percy Jackson and female Poseidon fanfiction is 'Poseidon's Daughter'. It has a great plot where the female character, as Poseidon's daughter, embarks on a journey similar to Percy's but with her own unique challenges. The author does a good job of integrating the character into the existing Percy Jackson universe.
The allure lies in the fact that Percy already has a very interesting backstory. As the Champion of Poseidon, fanfiction writers can expand on his powers and his place in the mythological world. For instance, he could be sent on quests that are specifically related to Poseidon's domain, like protecting a sacred sea temple from an ancient evil.
In fanfiction, their relationship could be developed by having Poseidon be more involved in Percy's daily life. Instead of just popping in during big events, he could be there for the small things too. For instance, helping Percy with his schoolwork that involves marine biology. They could also have a project together like building a new safe haven for sea nymphs. Through this, they would bond over creating something positive. Also, Percy could start to take on some of Poseidon's responsibilities in the ocean, with Poseidon guiding him. This would not only strengthen their bond but also show Percy growing into his role as Poseidon's son.
One plot idea could be that the fem Percy Jackson discovers a hidden underwater realm ruled by Poseidon that no one else knew about. She has to navigate through its mysteries and face challenges specific to that place, all while having a complex relationship with Poseidon that develops into a lemon - themed encounter in a very unexpected way. Maybe there are unique sea creatures there that play a role in their relationship development.
A powerful water nymph could be the main antagonist. Maybe she's jealous of the special bond between Percy and Poseidon and the power of the lemon. So she tries to steal the lemon and use its power to take over Poseidon's domain.