I really liked 'Fem Percy: Hades' Legacy'. It delved into her powers as the daughter of Hades. Since she's female, she might use her powers in a different way than the original Percy. She could be more in tune with the underworld's female spirits and use that connection to her advantage in battles and quests.
One great fanfic could be 'The Daughter of Poseidon's Journey'. It follows the female Percy Jackson as she discovers her powers in a new and unique way compared to the original male Percy. She has to face the same old monsters but with her own spin on dealing with them.
You can start by giving her a distinct personality. Maybe she's shy because she's always been feared for her father's sake. Then, gradually show her growing confidence as she discovers her own strengths. For example, if she has the power to raise small skeletons as minions, at first she's scared of it, but later she learns to use it for good. Also, explore her relationships with other characters. Her friendship with Percy could be based on mutual understanding of being different among the demigods.
Well, one unique plotline could be her relationship with her father, Hades. In some fanfics, she might be trying to earn his respect in a different way than a male Percy would. For example, she could use her femininity to her advantage in the Underworld politics.
One idea could be that the daughter of Hades has the power to communicate with the dead in a unique way, like seeing their memories. She could use this to help Percy solve a mystery that involves an ancient curse. Another plot could be her struggle to fit in among the other demigods because of her dark powers and the stigma associated with Hades. Maybe she discovers a hidden power within herself that is related to her father's realm and has to learn to control it while also dealing with the outside world's view of her.
To develop her character, start with her appearance. Maybe she has dark, almost black hair like the shadows of the Underworld and pale skin. For her personality, she could be a bit of an outcast among the other demigods due to her father. This might make her a bit brooding but also determined to prove herself. Give her some quirks, like she always wears a small charm that was a gift from Hades.
One great fanfic is 'The Female Percy in Young Justice's World'. It combines the elements of Percy Jackson's powers and the Young Justice universe really well. The female Percy is a strong character, facing challenges from both the demigod world and the superhero world in the story.
One great fanfiction you could check out is 'The New Quest' where female Percy and male Annabeth have to face an ancient evil that has resurfaced. It has some really interesting character dynamics as they navigate their relationship in a different gender setting.
There's a fanfic where Percy becomes a gunslinger to fight against an ancient evil that has invaded the Wild West in the Percy Jackson universe. It's filled with action-packed scenes and some really cool interpretations of how Percy's demigod abilities work in this new context. It's quite exciting to read.
There's 'Bisexual Percy: His Hidden Side'. This one focuses more on Percy's internal struggle. It's written in a way that makes you feel like you're right there with him. The author does a good job of showing how Percy's bisexuality is a part of him that he's been suppressing due to the expectations around him in the demigod world.
One great Percy Jackson Helios fanfiction is 'The Sun's New Champion'. It's really interesting as it explores a scenario where Percy has to team up with Helios in a quest. The author does a great job of mixing the two characters' personalities and powers.