In a fanfiction where Percy Jackson travels to the past, he might try to prevent some of the tragedies that occurred in the past. For example, he could attempt to stop the first Titan War from starting. He might use his skills and knowledge from the present to change the course of history, but this could also have unforeseen consequences, like disrupting the timeline and creating alternate universes.
Annabeth could definitely be one of his allies. She's smart and resourceful, and her knowledge of architecture and strategy would be useful no matter where in the universe they are. She could help Percy figure out the layout of strange alien cities or fortresses.
In fanfiction, Percy's trip to the past could make him more empathetic. Meeting his ancestors or seeing historical events unfold might make him understand the struggles and joys of those in the past. This new - found empathy could change the way he interacts with people in his own time. He could also become more cautious as he sees the consequences of actions in the past and realizes how his own actions in the past (while he's there) could impact the future.
His unexpected ally could be a minor god from the past. Maybe a god that was forgotten in his own time but still has some power in the past time period Percy travels to. This god could help Percy because they see an opportunity to regain some status through Percy's actions in the present time. Another possibility is an enemy from his own time who has different motives in the past and ends up working with Percy.
He might encounter advanced technology that he has no idea how to use. For example, flying cars or holographic communication devices. It would be really funny to see him struggle with these new things at first.
In this fanfiction, Percy might encounter alien species with unique powers. For example, he could meet a race that can control time, which would lead to some really exciting adventures as he tries to navigate through their time - warped worlds while also dealing with his own demigod powers.
He could meet his parents when they were young. Maybe he'd get to see his mother before she met his father and understand more about her life back then.
In this fanfiction, Percy might have adventures like battling mythical creatures in the Amazon rainforest. He could encounter new demigods and form alliances to face powerful foes.
Well, considering past heroes are from different eras, they wouldn't have had the opportunity to read Percy Jackson fanfiction. Percy Jackson is a modern creation, and fanfiction about it is part of today's digital and literary culture. Past heroes were busy with their own heroic deeds and didn't have the Internet or knowledge of such modern fictional concepts.