It could be a mark that represents his family or a long - lost heritage. Perhaps it's a crest that has been passed down through generations in his family but he has to keep it secret for some reason, like it might draw unwanted attention from certain enemies or factions in the story.
The idea of Percy having a secret girlfriend in fanfiction can open up a whole new world of character development. If his girlfriend is a new character introduced in the fanfiction, she could have unique powers or abilities that complement Percy's. Their secret relationship could be a way to explore Percy's more private and vulnerable side, away from his usual heroic adventures.
Perhaps the tattoo has a special meaning that he wants to keep private. It could be related to a personal journey or a relationship that he doesn't want others to interfere with. For example, if it's a tattoo related to a past love or a mentor who taught him a valuable but forbidden skill. The knowledge of the tattoo could expose these things and he wants to protect them.
His secret girlfriend could be in a difficult situation herself. Maybe she's a demigod with a dangerous family or past. Percy is trying to help her while keeping their relationship a secret. This could involve them sneaking around to meet, sharing secret glances in public, and having to communicate in coded ways. It would create a really interesting and suspenseful plot.
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.
One possibility could be that Percy has been leading a double life. Maybe he had a relationship in the past that he kept hidden, and now the existence of the child is coming to light. The story could explore how he copes with this new reality and how it affects his relationships with his friends and family.
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.
Maybe there is a shadowy organization that is against the existence of Percy's secret life. They view it as a threat to their own plans and will stop at nothing to eliminate Percy and his secret world.
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.
Perhaps Percy's secret life is that he is a time - traveler. He uses his ability to go back in time to fix mistakes or prevent disasters, but he can't let anyone know as it could disrupt the timeline.