He could meet his younger self. This would be a really interesting encounter as he could either try to guide his younger self or be shocked at how different he was back then. Another possibility is meeting some of the ancient heroes that he only heard about before. For instance, he might come across Hercules and learn from him.
Percy could meet the early founders of Camp Half - Blood. He could witness how the camp was first established and perhaps offer his help in making it better from the start. He might also meet some of the gods in their younger forms. Zeus, for example, when he was still more impulsive and less in control. This would be a very different experience from dealing with the more 'mature' Zeus in the present time.
In such a fanfiction, Percy might use his knowledge of the future to change some key events in the past. For example, he could prevent some of the earlier disasters or conflicts in the Percy Jackson universe. Maybe he'd try to stop the first encounter with a certain monster in a different way to avoid the chaos it caused.
He might meet Luke before he turned bad. Percy could try to change Luke's fate, convince him not to follow Kronos. It would be a great chance to save a friend and prevent a lot of the chaos that happened later.
His water - based powers might be affected in different ways. If he goes back to a time when the oceans were less polluted, the purity of the water could make his powers stronger. However, if he goes to a time when the gods were more in control of the elements, they might be able to limit his power. For example, Poseidon might have more say over how Percy can use water powers if they are in the same time period.
One interesting plot idea could be Percy going back in time to the era of the Greek heroes. He could meet Hercules and learn from him. Maybe he would have to face the same challenges Hercules did, but with his own modern - day skills and knowledge. Another idea is that he goes back to the time when the gods first emerged and gets involved in the power struggles among them. This could change the entire course of mythology as we know it.
Percy might run into his old friends' ancestors. This could create some really strange and exciting interactions. For instance, if he meets an ancestor of Annabeth, he could learn things about her family history that she doesn't even know.
It could be an ancient and powerful Titan who was thought to be defeated long ago. Since Percy is in the past, this Titan could be in his prime and see Percy as a threat to his plans of ruling over the world again. For example, Kronos might be even more powerful in this past era and Percy has to find a way to stop him without the help of his modern - day friends.
Percy might encounter Baba Yaga. She is a well - known figure in Russian folklore. She could be an adversary, testing Percy's skills and his knowledge of the magical world. Or perhaps she could be a source of information if Percy manages to earn her respect. He could also meet the Rusalki, water nymphs from Russian mythology. Given Percy's connection to water, it would be interesting to see how he interacts with them.
He could meet some Aboriginal heroes or spirits. They might have their own powers and knowledge that Percy can learn from.
He might meet some native Alaskan spirits. These spirits could be like the nature spirits he has encountered before but with their own unique Alaskan characteristics.
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.