Well, she could be the main character in a story where she discovers a long - lost power within herself. This power could attract the attention of both good and bad forces. Maybe she gets involved in a power struggle within the underworld, with some of the other powerful entities trying to either use her or stop her from using this new power. Also, a fanfic about her exploring different realms and making unexpected friendships along the way would be cool.
One idea could be a story where Hades' daughter ventures into the mortal world and has to hide her true identity while falling in love with a mortal. Another could be her going on a quest to prove herself to her father. Or perhaps a fanfic where she teams up with other mythological beings to save the underworld from a new threat.
In a hades daughter fanfic, it could be interesting if she was sent on a mission by her father to the overworld to retrieve a stolen artifact. During this mission, she meets a group of heroes who are initially suspicious of her but then come to realize she has good intentions. As she tries to complete her task, she has to deal with the cultural differences between the underworld and the overworld, and also face her own insecurities about being Hades' daughter and whether she can live up to his expectations.
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.
One plot idea could be Hermione discovering her true parentage gradually. Maybe she starts having strange powers related to the underworld that she can't explain. For example, she could have an ability to communicate with the dead, which at first scares her but then she realizes it's a part of her heritage from Hades. Another idea is that she has to deal with the reactions of her friends, especially Harry and Ron. They might be shocked and a bit scared at first, but eventually come to accept her for who she is.
One interesting plot idea could be her struggling with the stigma associated with being Hades' daughter. For example, other demigods might be scared or distrustful of her at first. Another could be her going on a quest related to the Underworld, like trying to stop some escaped souls from causing chaos on Earth. She could also have a special power related to the dead that she has to learn to control, such as being able to see the last moments of a dead person's life, which could be both a gift and a curse as she might see some really traumatic things.
One idea could be Percy discovering new powers related to being the son of Hades. For example, he might be able to control the shadows in a unique way that no other demigod can. He could use this power to spy on enemies or to travel quickly through the underworld.
Perhaps a plot where Hades and Persephone have to prove their love to a council of the most ancient gods. They are given a series of tasks, like Hades having to bring light to a part of the Underworld without using the sun, and Persephone having to make a barren part of the Underworld fertile again. Through these tasks, their love deepens and they also gain more respect from the other gods.
Maybe the son of Hades in the fanfic has a special bond with a particular type of monster that is usually associated with death, like a Cerberus - like creature. Percy Jackson and his friends are initially scared of this bond but then realize it could be used to their advantage. For example, the son of Hades could use this bond to control the monster and have it help them in a battle against a common enemy. The fanfic could also explore how the son of Hades tries to fit into the world of Camp Half - Blood while being different from the other demigods.
Another plot idea is that there's a rift in the House of Hades that is slowly corrupting the place and they have to find the source of it. Along the way, they face their own inner demons. Annabeth might struggle with her insecurities about being smart enough to solve the mystery, while Percy battles with his fear of not being strong enough to protect Annabeth. As they overcome these personal struggles, they also get closer to solving the problem of the rift.
A possible plot is that the daughter is sent on a quest to find a lost artifact that is crucial for the balance of the ocean. Along the way, she discovers secrets about her family's past that her father has been hiding from her. This could lead to some tension between them, but also help her grow as a character. She could also face challenges from other Atlantean factions who don't believe she is worthy of this task because she is still young and inexperienced.
One idea could be Percy discovering his unique heritage as the son of Hades and Persephone and struggling to fit in among the other demigods. He might have powers related to the Underworld that set him apart, like the ability to control certain types of plants that grow in the Underworld. Another plot could involve him having to deal with the politics between the gods because of his parentage. For example, Zeus might be suspicious of him due to his connection to Hades.
One idea could be exploring Persephone's adjustment to the Underworld. For example, she could start a garden in the gloomy realm using her powers over plants, which not only changes the look of the Underworld but also the attitude of its inhabitants. Another plot could be Hades trying to court Persephone in a more modern way, like taking her on a tour of different parts of the Underworld that are beautiful in their own dark way.