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.
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.
Perhaps a plot twist could involve Kronos' essence trying to take over Percy's body. Percy would have to fight against this internal takeover, and in the process, he discovers a way to use Kronos' power for good. This would completely change the dynamics of the Percy Jackson universe as we know it, with Percy becoming a sort of anti - hero figure who uses the power of the enemy to protect his friends and the world.
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.
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.
Well, in a 'Percy Jackson Seventh Son of Kronos' fanfiction, the plot could center around Percy being hunted by both the gods and the Titans. Since he's the seventh son of Kronos, he has a unique power that both sides want to either control or destroy. Percy has to go on a quest to find a way to neutralize this new aspect of his identity so he can live in peace. Along the way, he teams up with some unexpected allies, like a group of demigods who are also outcasts for various reasons.
In these fanfictions, the theme of acceptance is quite common. Percy has to come to terms with being the son of Kronos and Hestia, and the demigod community also has to accept this new reality. Redemption can also be a theme in some cases. If Kronos' dark past is considered, Percy might have to deal with the idea of redeeming his father's name in some way. And of course, adventure is always a theme in the Percy Jackson universe, and these fanfictions are no different. With his new parentage, Percy embarks on new and exciting adventures that are different from the ones in the original books.