In the fanfiction, Kronos may torture Percy simply because of his power. Percy is a very powerful demigod, and Kronos may be jealous or afraid of that power. By torturing Percy, he might be trying to strip him of his power, either literally or figuratively. Additionally, Kronos could be torturing Percy as part of a larger scheme to disrupt the balance in the demigod world. If Percy is out of the picture, either broken or dead, it will be easier for Kronos to carry out his evil plans.
Some fans might write this type of fanfiction as a form of catharsis. They may have had certain emotions or ideas related to the characters that they want to express in a more extreme way. Also, it could be a way to explore the moral and ethical boundaries within the Percy Jackson world. By having Annabeth torture Percy, it forces the readers and the writer to think about what is right and wrong in that fictional context, and how the characters would be affected by such actions.
In fanfiction, Percy could become a champion of Kronos due to a complex web of factors. It could start with his disillusionment with the Olympians. After all the battles he's fought for them, if he sees no real change in how they treat demigods or the world in general, he might be open to an alternative. Kronos, being a master manipulator in these alternate stories, could offer Percy power and a chance to truly make a difference. Also, Percy's relationships could play a role. If someone he trusts sides with Kronos and convinces him, or if he's in a situation where he has no other allies and Kronos offers support, he could end up in that role. But these are all departures from his original character in the official Percy Jackson series.
One possible plot could be Percy starting off reluctantly working for Kronos. Maybe Kronos has some sort of leverage over Percy, like threatening his friends or family. Percy then has to play a double - agent role, secretly trying to undermine Kronos' plans while appearing to be loyal. He could gather information about Kronos' forces and weaknesses and pass it on to the good guys.
One possible plot could be that Percy discovers his true relation to Kronos early on. This revelation could cause a great deal of inner turmoil as he has to come to terms with being related to the main villain. He might then struggle with whether to side with his friends or his new - found brother, creating a complex moral dilemma.
One possibility is that Kronos captures Percy to steal his powers. Percy, being a powerful demigod, has abilities that Kronos desires for his own evil plans. While captured, Percy may discover some secrets about Kronos' past that could be used against him. He has to use his wits and any small resources he has in the prison to outsmart Kronos and break free.
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.
Some of Kronos' minions, like the monsters he commands, could be antagonists. For instance, the dracaenae. They are always eager to prove themselves to Kronos and might see Percy as competition within Kronos' ranks. They could constantly try to undermine Percy's position and cause trouble for him.
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.
Well, one possible plot could be Percy having to hide his relation to Kronos while still fighting against the Titans. He might struggle with the internal conflict of having a connection to such an evil entity as Kronos while trying to protect his friends at Camp Half - Blood.
Well, Kronos is a very powerful and evil figure. If he takes over Percy in fanfiction, Percy might be forced to do a lot of bad things against his will. His friends would likely be in great danger as Percy, under Kronos' control, could turn on them. Kronos could use Percy's powers to cause chaos and destruction in the world of the Gods and demigods.