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.
It could be a jealous rival of Twilight. Maybe someone who has always been envious of her status and power in Canterlot.
It could be a jealous demigod. Maybe someone who is envious of Percy's popularity and Nico's unique powers. This person might see an opportunity to get rid of them and take their place in the demigod hierarchy.
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.
Definitely Annabeth. Since she has a strong connection with Percy already, in a time travel scenario, she could be one of the main characters in the harem. Also, Piper could be there. Her charm - speak ability might play an interesting role in the harem dynamics. And perhaps some of the minor female characters from the series like Silena Beauregard could also be included if Percy travels to a time when she was still alive.
A Kronos - like figure could be a likely villain. If someone were to time - travel and accidentally free a younger, more malevolent version of Kronos, he could cause all sorts of chaos. He has a grudge against the Olympians and would stop at nothing to regain his power.
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.
If Annabeth betrays Percy in fanfiction, it would likely shatter Percy's trust. He has always relied on her, and this would be a huge blow. He might become more withdrawn and less likely to trust others in the future.
Well, in fanfiction, Percy could be betrayed by his love interest. Imagine Annabeth suddenly siding with an enemy because she was somehow mind - controlled. This would be a huge betrayal for Percy, and the abuse could come in the form of emotional pain as he struggles to understand why she has turned against him.