Another option could be a goddess in disguise. For example, a water - related goddess who has a connection with Percy. This would bring in some interesting divine elements to the fanfiction.
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.
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.
Annabeth could be the mother. Since she and Percy have a strong relationship in the original series, it's very likely that in a fanfiction they would have a child together. Their combined intelligence and Percy's powers would make for an interesting genetic combination for their child.
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.
It could be Aphrodite. Given her domain of love, it would be an interesting take. Percy might be charmed by her beauty and grace, and they could end up having a child. The child might inherit Aphrodite's charm and Percy's courage.
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.
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.
The child could be an orphan from a far - off land that Percy visited. Maybe Percy found the child alone and starving, and felt responsible for the child's well - being, so he brought the child back.
The child could be a prophesied one. In the world of Percy Jackson, prophecies are common. So, this child could be the one foretold in some ancient prophecy that is linked to Tartarus. Percy finding the child sets off a chain of events that will either save or doom the world. Maybe the child is the key to closing a portal in Tartarus that is releasing evil into the mortal world, and Percy is the only one who can help the child fulfill this great task.
The child could be a young demigod who got lost on a quest and ended up in Tartarus. Maybe they were trying to prove themselves and got in over their head.