The Olympian gods could be the main antagonists. Since Percy is the adopted son of Kronos, they might see him as a potential threat and try to stop him before he can fulfill any of Kronos' possible plans. They may send their demigod heroes after him.
Yes, there are likely fanfictions out there with this concept. Fanfiction writers often explore alternative storylines and relationships. However, it goes against the canon as in the original 'Percy Jackson' series, Percy is the son of Poseidon. But in the world of fanfiction, anything is possible.
One idea could be Percy struggling with the dark influence of Kronos while still trying to maintain his loyalty to his friends at Camp Half - Blood. Another could be Percy having to hide his true identity as Kronos' adopted son from his closest allies. Maybe he discovers some long - lost powers or knowledge that Kronos had hidden away for him, which he must use to either save or destroy the world of the gods.
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.
Well, in such a fanfiction, Percy's character arc would be completely transformed. Instead of having the connection to the sea like in the original where he's Poseidon's son, he might have a connection to time or something related to Kronos' powers. His relationships with other characters would also be different. For example, his friendship with Annabeth might be strained as she might see him as a threat due to his new 'parentage'. The story could be filled with internal struggles as Percy tries to come to terms with who he really is and the legacy of Kronos.
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.
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 this fanfiction, there might be a lot of focus on Percy's relationship with the other wolves in Lupa's pack. He could learn their ways of survival, their hierarchy, and how to be a part of their community. This would be a great way to explore his adaptability and growth.