She could be a completely new character created just for this fanfiction. Maybe she's a normal human girl who Percy discovers has a connection to the world of the gods in some way.
She could be the daughter of a minor god that has been forgotten or shunned. For example, the daughter of Hecate's lesser - known cousin who has some magic abilities but no real place in the demigod world until Percy takes her in.
The plot might involve Percy's journey in becoming a father figure. He would have to learn how to take care of a child, which is completely different from his usual adventures. He might face challenges like dealing with the girl's school, her making friends, and also protecting her from any threats that come his way because of his own past or the girl's special circumstances. For example, if she's a demigod too, there could be monsters after her.
One possibility is that Percy discovers a young demigod girl in a dangerous situation, like being chased by monsters. He decides to take her under his wing and protect her. They then embark on a journey to Camp Half - Blood, facing various challenges along the way.
In this fanfiction, the plot could involve Percy initially being hesitant to adopt Sally's daughter. But as he gets to know her, he realizes she has a lot of potential and a great heart. He starts to provide for her, like getting her into a good school if it's a modern - setting story. And they could go on adventures together, facing challenges that strengthen their bond.
It could be Sally's ex - partner if there was a not - so - nice one. This person might want to take the daughter back out of spite or some wrong idea that Percy isn't a good enough caretaker.
One idea could be that Percy discovers a demigod child who has been abandoned in the mortal world. He decides to adopt the child to protect them from monsters and to give them a proper home at Camp Half - Blood. He then has to teach the child about their demigod heritage and how to use their powers.
One common theme is mentorship. Apollo often takes on the role of a mentor to Percy, teaching him about different aspects like new powers or knowledge. For example, in many stories, Apollo teaches Percy about the arts which Percy is not very familiar with initially.
Maybe Percy discovers a kid in a difficult situation, like being an orphan in a monster - infested area. He decides to take the kid under his wing to protect him from harm.