In some fanfictions, a plot twist could be that the world they know is actually an illusion. They are fighting in a false reality created by an enemy. When they discover this, they not only have to find a way to escape but also figure out how to fight the real enemy in the real world. Another interesting twist could be that their powers are amplified in a strange way. For example, Percy's water powers start to affect not just water but all liquids, including blood. And Jason's lightning powers start to control electricity in all forms. This would make their fight even more unpredictable and exciting.
A great plot twist could be that they are both being manipulated by a third force. They think they are fighting each other for their own reasons but in reality, they are being used. Maybe a god or a powerful demigod is pulling the strings. This would lead to a moment of realization and then they would have to figure out how to work together to stop the real threat. Also, a plot twist where the Mark of Athena has a different meaning for each of them could be really engaging. It could be that Percy thinks it means one thing and Jason thinks it means another and their interpretations lead to a big misunderstanding before they figure it out.
One interesting plot twist could be that Annabeth discovers a hidden power within herself that has nothing to do with Athena. Maybe she can suddenly communicate with mythical creatures in a way no one else can. Another could be Percy finding out that he has a long - lost sibling who is actually on the side of the enemy, but then later switches sides. And a third one might be that the Mark of Athena is actually a fake, created by an enemy to mislead the demigods and lead them into a trap.
In my opinion, it's really hard to say who would win. Jason has his Roman powers which are quite formidable, like his ability to control the winds. Percy, on the other hand, has his water - based powers which are extremely powerful especially in the right environment. In a fanfiction, it could really go either way depending on how the author wants to write it. Maybe they could end up not really fighting but joining forces against a common enemy.
One idea could be a new quest where Percy and Annabeth have to find a lost artifact related to Athena that was stolen by a rogue demigod. This would involve them traveling to new and dangerous places, facing off against mythical creatures they haven't encountered before.
One popular plot twist is when they end up swapping powers. Percy suddenly has control over wind and lightning while Jason can control water. This flips the script and makes for some really interesting scenarios.
One interesting plot twist could be that Percy discovers a way to nullify Kratos' god - given powers. Maybe he finds an ancient artifact during the fight that has the ability to do so. Another could be that Kratos, instead of seeing Percy as an enemy, realizes they have a common goal against a greater evil in the fanfiction world and they end up teaming up.
Another possible plot twist is that their sparring somehow awakens an ancient prophecy. They initially think it's just a normal sparring session, but then strange signs start to appear. For example, old symbols start to glow on the ground around them as they spar. They then have to figure out what this prophecy means and how their sparring is related to it, all while still dealing with their friendly competition.
One interesting plot could be a competition between them for a powerful magical artifact. Percy uses his water - based powers, Jason his lightning and flight, and Nico his control over the dead to outwit each other in a race to find it.
Well, it could be that there's some sort of magic or illusion at play. Jason might be seeing Percy as a god because he's been influenced by an external force. This external force could be an enemy trying to create chaos by making the other demigods believe Percy is a god. And Percy has to then figure out what's going on and clear his name while also dealing with the new - found respect or fear from his peers.
One interesting plot twist could be that they find out they are related in some way through the complex web of mythology. Maybe there's a long - lost ancestor who was part of both Greek and Norse worlds. Another could be that they are forced to swap powers. Percy has to deal with Magnus's Norse magic and Magnus has to handle Percy's water powers. It would be really cool to see how they adapt.
One possible plot twist could be that the gods oppose the marriage. Since Athena is a virgin goddess in Greek mythology, her getting married would go against the traditional view of the gods. This could lead to a conflict where Percy has to prove himself worthy not only to Athena but also to the other deities.