There's also the possibility that it could be an original character created just for the fanfiction. This would give the writer more creative freedom to shape the story around the relationship between Batman and the mother, and how it impacts their son.
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.
In some fanfictions, the mother could be an original character created by the author. This allows for a lot of creative freedom in developing the backstory and relationship dynamics.
In many fanfictions, Sakura could be a potential mother. Since she has a close relationship with Naruto in the original series, some fans might imagine a scenario where they end up together and have a son. Another possibility could be Hinata. Given her deep love for Naruto, it's not hard to fathom a fanfiction where they have a secret son.
In fanfiction, Batman having a son could lead to many interesting stories. Maybe the son discovers his father's secret identity early on and has to deal with the pressure of living up to the Batman legacy. He might also have his own unique powers or skills that set him apart from Batman, leading to a dynamic where they both learn from each other.
It could be a northern girl, someone who Brandon met during his travels in the North. Maybe she was a daughter of a minor lord, and they fell in love while he was on a mission to secure the North's borders.
It could be Hinata. Even though in the original story they are openly married, in a fanfic scenario, there could be a situation where their relationship was kept secret for some time and she gave birth to a son secretly. Maybe due to some threat to the village or Naruto's safety.
It could be Renesmee. Since she has a connection with Jacob in the Twilight series, it's not a stretch to think that they might end up having a child together in a fanfic. Their relationship was already quite complex and a child would add another layer of depth to it.
In this fanfiction, the mother could be a powerful sorceress. She used her magic to create a baby with Kratos' essence for some grand purpose. But then she disappeared, leaving Kratos to deal with the baby. This would add an interesting layer of mystery to the story as Kratos tries to figure out why she did it and what the baby's true nature and purpose are.
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.
Perhaps it could be a character from an alternate dimension. In some fanfiction scenarios, portals open between different dimensions, and Spiderman could have had an encounter with a female character from another world, which led to the baby.