We should avoid seeking out 'dirty' fanfiction. The Percy Jackson series is aimed at a wide audience, including young readers, and the relationship between Percy and Annabeth is meant to be a positive example of friendship and love. If you want to read fanfiction about them, look for stories that uphold these values, such as those that explore their heroic deeds together or their personal growth within the context of their relationship.
I cannot recommend or direct you to find inappropriate fanfiction. It is better to focus on fanfiction that respects the integrity of the characters and the original story. For positive Percy and Annabeth fanfiction, try searching on popular fanfiction platforms and filtering for high - rated and well - reviewed stories that are centered around their relationship in a positive way.
There are many great Percy and Annabeth fanfiction out there that don't involve 'dirty' content. These can be found on platforms like Wattpad. On Wattpad, you can search for Percy and Annabeth fanfiction and find stories that focus on their love story, their adventures, and how they complement each other. It's a much better alternative to seeking inappropriate content.