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.
Maybe Percy leaves camp to protect his loved ones. He meets someone special during his journey and they have a daughter. He then has to raise her while also dealing with the threats from his past life at the camp.
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.
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.
Percy would use his combat skills. He has a lot of experience in fighting monsters, so if any threats come near his daughter, he'd be ready to fight them off with his sword. He'd also use his strategic thinking to outwit enemies.
He might meet other demigods who are not affiliated with the camp. These could be demigods who have been living on their own, trying to hide from the monsters and the chaos of the demigod world. They could have different views on how to use their powers and might teach Percy new ways to fight or survive.
Percy might be a simple guy who just fell in love with a Canadian girl he met online. So, he decides to leave his place and go to Canada to be with her. He has to face the uncertainties of long - distance relationships becoming real - life ones, and also adapt to the new environment where his love lives.
He might go on a solo adventure to discover more about his powers. He could encounter new mythical creatures that he hadn't seen around the camp. Maybe he'll meet some other demigods who are on the run or have their own secret quests.
It could be an original character created just for the fanfiction. Maybe a mysterious ninja woman who crossed paths with Kakashi during a mission and they had a brief but intense relationship.
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.