It could be Luke. Even in a time - travel scenario, Luke's bitterness towards the gods might lead him to betray Percy. He could use time - travel to his advantage, perhaps making deals with past versions of enemies to stop Percy from achieving something that would benefit the gods.
There's also the possibility that Chiron could be the betrayer in a very unexpected twist. Maybe in a different time - line during the time - travel, Chiron has been corrupted or forced to betray Percy due to some dark magic or external threat. This would be a huge shock to Percy as he has always trusted Chiron as a mentor.
A new character introduced during the time - travel part could be the betrayer. Maybe a demigod from a different era who seems friendly at first but has their own hidden agenda. They could pretend to help Percy with his time - travel mission but then betray him when it suits their goals, like stealing a powerful artifact that Percy was supposed to protect.
Luke might be the one to betray Percy again in a fanfiction. Even if he had a change of heart before, perhaps in this fanfiction he's been influenced by some dark force once more. He could pretend to be on Percy's side and then stab him in the back when Percy least expects it.
Another possibility is that it could be a character who has been corrupted by dark magic. This character was once a friend or at least an acquaintance of the dragon rider. But the dark magic makes them see the dragon rider as a target. They betray the rider in the hopes of getting some sort of power or reward from a more powerful evil entity.
One great 'Percy Jackson Time Travel Fanfiction' is 'Time Warped'. It takes Percy back to ancient Greece and he has to deal with all kinds of challenges that are different from his modern - day ones. He meets his ancient relatives and has to figure out how to get back to his own time without changing history too much.
One great 'Time Travel Percy Jackson Fanfiction' is 'The Time - Traveling Demigod'. It has an exciting plot where Percy is sent back in time and has to deal with all kinds of challenges that change his understanding of his own world. The author does a great job of keeping Percy's character consistent while also showing how he grows through these new experiences.
One idea could be Percy accidentally travels back in time and encounters Chronos in his prime. Maybe he has to team up with some of the old - time demigods to stop Chronos from an early attempt at world domination. It would be full of action and adventure as Percy tries to use his modern skills in an ancient world.
To write a great 'Percy Jackson Time Travel Fanfiction', think about the consequences of time travel. If Percy changes something in the past, how will it affect the present and future? You can also add some unique twists. For instance, what if the time - travel device malfunctions and he keeps bouncing between different time periods? And don't forget to include the humor and adventure that are typical of the Percy Jackson series.
In many Percy Jackson fanfictions, time travel often works through magical artifacts. For example, a special time - turning hourglass might be used. It could be a powerful object left behind by an ancient god or goddess.
Percy could change the past and accidentally create a new future. For example, if he stops Chronos from a certain event, it might have unforeseen consequences for the demigod world he knows. He might return to his own time to find that his friends are different or that Camp Half - Blood has changed drastically.
He could be portrayed as a time - bender, having the power to not only travel through time but also manipulate it to some extent. For example, he could slow down time during battles in the past to gain an advantage.
It could be an enemy in disguise. Maybe a Grimm has managed to infiltrate their ranks in a clever way and then betrays the Rose character. Grimm are known for their devious ways and this would be a very RWBY - like scenario.