Well, in this fanfiction, Percy might face a huge moral dilemma. Since Kronos is a villain, Percy joining him could be a really dark turn. Maybe he's been tricked or is trying to stop Kronos from the inside. It could lead to some intense battles within the Titan's ranks as Percy tries to figure out his true loyalties.
If Percy Jackson joins Kronos in fanfiction, it would be a huge deviation from the original story. Percy is a hero who stands for good, and Kronos is a villain. This could lead to a very dark and twisted version of the Percy Jackson universe, with Percy using his powers to aid Kronos in his evil plans, perhaps causing chaos among the gods and other demigods.
Percy's reaction could also be one of self - doubt. He may start to question his own actions and leadership. He might think that he has done something wrong to push Annabeth away. However, his loyalty to his friends and the cause would eventually make him stand up against Kronos and try to bring Annabeth back to the right side.
When Percy joins Kronos in the fanfiction, it affects the other characters in many ways. Chiron, the centaur mentor, would be deeply disappointed. He had so much hope for Percy. The minor demigods who looked up to Percy would be lost. They might lose faith in the idea of being a hero. The relationships that Percy had built over the years would be shattered. His joining Kronos would also make the enemy stronger, which would put more pressure on the remaining good characters to come up with a plan to stop them both.
The story would be very different. The loyalty of the other characters would be tested. For example, Annabeth might be heartbroken and try to bring Percy back to the right side. Also, the gods would be in a much more difficult situation as they face a combined threat of Percy and Kronos.
In a fanfic scenario where Percy Jackson joins Kronos, it could be a very interesting exploration of the 'what - ifs'. Percy has a strong sense of justice, so for him to side with Kronos, Kronos must have presented a very convincing argument. It could be that Kronos showed Percy a future where the demigods are constantly oppressed by the Olympians. However, this would also mean Percy has to go against his instincts and the relationships he has built. His friends like Annabeth would be in shock and try to bring him back to the right side. This could lead to some intense battles not only between the demigods and Kronos' forces but also within Percy himself as he struggles with his new allegiance.
In many fanfictions, Percy might use his water powers in a unique way. Maybe he combines his control over water with his sword fighting skills. He could create a giant water vortex to disorient Kronos and then strike with Riptide while Kronos is off - balance.
Maybe there are some original characters created by the fanfiction author. These characters could have their own unique abilities and backstories. They might be the ones who tip the scales in Percy's favor, for instance, by having a special power that weakens Kronos just before Percy makes the final blow.
Luke could also be a prominent character. Since he has a complex relationship with Kronos in the original story, in fanfiction he could play a role in either helping or hindering fem Percy's efforts against Kronos. Nico di Angelo is another possibility. His powers over the dead could be useful in a fight against Kronos, and he might team up with fem Percy for that reason.
One possible reason could be that Kronos has somehow tricked her. Maybe he promised her something she desperately wanted, like power to protect her loved ones in a way she thought Percy couldn't. Another reason might be that she was brainwashed. Kronos could have used some dark magic or manipulation to make her believe that Percy was on the wrong side.