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.
Perhaps she's the daughter of a demigod who died heroically. Percy feels responsible for her because of his own experiences and the fact that he wants to give her a chance at a normal demigod life. She could have inherited some of her parent's powers but also their enemies.
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.
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.
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.
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.
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.
Percy Jackson himself could be an ally. Despite their differences, they both have a common goal of protecting the demigod world. His skills in combat and her intelligence would make them a great team.
There could also be a group of rogue demigods who oppose the daughter of Artemis. They might be jealous of her powers or her connection to Artemis. They could try to sabotage her and Percy's quests and cause trouble for them at every turn.
Well, it could be about the daughter of Zeus trying to fit in at Camp Half - Blood. Maybe she has powers that are hard to control, like being able to summon huge lightning bolts at unexpected times. She might struggle with the expectations that come with being the daughter of the king of the gods.
The plot could involve her on a quest. Maybe she's searching for a way to break the cycle of Kronos' evil. She might team up with Percy Jackson and other characters. They could face various monsters and challenges along the way. And she could be constantly battling her own inner demons related to her father's nature, like a tendency towards power - hunger that she has to overcome.
The Titans could be great antagonists. They might see the daughter of Hecate as a threat to their plans of taking over. Her magic could be something they want to either control or destroy.