The mother could also be a completely new character created specifically for this fanfiction. She might be from a different realm or have some special powers. And her relationship with Percy could be a complex one, filled with secrets and misunderstandings that led to the situation of having a secret daughter.
It could be an old acquaintance that Percy had a brief relationship with. Maybe someone he met during one of his adventures and then lost touch with, but she later discovers she's pregnant and decides to keep the child a secret from Percy for various reasons.
Perhaps it's an old acquaintance from Percy's past who he reconnects with after leaving camp. They fall in love and she becomes the mother of his daughter.
It could be a random witch that Snape had a brief encounter with. Maybe she was someone he met during his time as a Death Eater or while he was spying for Dumbledore. She could have been a fellow Hogwarts student from his youth that he had a secret relationship with.
Perhaps the plot could involve Percy's daughter discovering her true identity on her own. She might start to notice strange things about herself or her father's behavior. For example, she could find some old letters or artifacts that hint at her origin. And as she digs deeper, she gets closer to the truth, which also brings her closer to the dangerous world her father has been shielding her from.
Maybe it could be a new character. A mysterious woman who Percy meets during one of his adventures. This would add an element of mystery to the story.
Annabeth could be the mother. Since she and Percy have a strong relationship, it would be a natural choice. Their son would inherit both their intelligence and combat skills.
It could be an original character created specifically for the fanfiction. Maybe a mysterious woman Jaune met during one of his adventures who he had a brief relationship with.
It could be an original character created just for this fanfiction. Maybe a girl who Stiles met during a summer vacation and had a brief fling with.
It could be Ginny. Even though in the original story they are married and have kids in a more normal way, in fanfiction, there could be a twist where their relationship had a secret earlier on and she is the mother of the secret child.
It could be a random villager that Naruto met during one of his travels. Maybe she was from a small village that Naruto helped protect, and they had a brief encounter that led to the child.