Obviously, Percy Jackson is one of the main characters. He is the central figure around whom the idea of 'betrayal' revolves. The son of Kronos is also a key character, as the one who feels betrayed by Percy. Other common characters might include Annabeth, Percy's girlfriend. She could be involved in either trying to clear Percy's name or getting caught in the middle of the conflict between Percy and the son of Kronos.
One possible story could be where Percy is framed for a crime he didn't commit against the son of Kronos, leading to his so - called 'betrayal'. Maybe he was set up to look like he stole an important artifact that the son of Kronos was supposed to protect.
To develop the character, start with his backstory. Since he's the son of Kronos, he might have grown up in a very different environment compared to other demigods. Maybe he was hidden away by a minor god who felt sorry for him. His past experiences of being alone and shunned because of his father would shape his personality, making him a bit of a loner at first.
In a fanfiction, Percy could face other demigods who are suspicious of him because of his relation to Kronos. He'd have to prove that he's not going to follow in Kronos' evil footsteps. Maybe he teams up with some unlikely allies, like a child of a minor god, to show his loyalty to the good side.
Annabeth is often a popular character. In fanfiction, she might play a crucial role in helping Percy deal with his complex identity as the son of Kronos. Grover could also be popular as he's Percy's loyal friend and could be there to support Percy through his struggles related to his new - found heritage.
In fanfiction, Kronos's role is not just limited to being a villain. Sometimes, he can be a catalyst for character development among the demigods. His actions force the heroes to become stronger, both physically and mentally. For instance, his threat might make Percy Jackson more determined to master his powers. Also, Kronos can be used to introduce new plot elements, like a new weapon or a magical item that has the power to stop him.
One great Kronos fanfiction could be about his backstory before he turned evil. Maybe it explores his relationship with the other Titans and what led him to start the war against the Olympians.
The plot could involve Percy being ostracized by the other demigods due to his relation to Kronos. However, he discovers a prophecy that only he, as the son of Kronos, can fulfill. This prophecy might be about saving the world from a new threat that is related to the Titans in some way. He then has to go on a quest to gather ancient artifacts or gain the trust of certain beings to be able to carry out the prophecy.
It could be the Titans who see Percy as a threat. Since he is the son of Kronos, they might want to either use him for their own purposes or eliminate him to prevent any interference in their plans.
One interesting plotline could be Percy having to deal with the conflict of being the son of Kronos while still being a hero. He might struggle with the dark legacy of Kronos within him. Another could be his relationship with Thalia evolving in unique ways, like they team up against a new and powerful enemy that threatens both their existences.