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.
He might become more cautious. Since the future is unknown and full of new things, he would have to be careful. For instance, he can't just rush into a fight without knowing what his opponents are capable of.
He could meet his future self. This encounter might be full of surprises as his future self could have different views and experiences. His future self might be more jaded or more powerful.
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.
Percy might meet an old enemy who has somehow been resurrected or changed in the future. This enemy could be more powerful and have a new plan to take over the world or destroy the demigods. Or he could meet a group of time - traveling demigods from an even further future who are trying to fix something in Percy's future that has gone wrong.
One possible plot could be that Percy discovers a magical device that sends him to the future. There, he might find a world that has been drastically changed by the actions of the gods in his time. Maybe the demigod camps have evolved into something completely different, and he has to adapt to new rules and powers.
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.
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.
Well, in Percy Jackson god future fanfiction, the characters could face all sorts of new challenges. Maybe the gods will demand more from Percy and his friends. They might have to deal with new monsters that are even more powerful. It could also be that the relationships between the characters change. For example, Percy and Annabeth might have to make some tough decisions regarding their future together, like whether to stay in the demigod world or try to live a normal life. There could be new alliances formed among the demigods too, to face whatever the future throws at them.