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 this fanfiction, it could be some of the Titans who are still loyal to Kronos' old ways. They might see Percy as a tool to bring back Kronos' full power. They would try to manipulate Percy into joining their cause, and when he refuses, they become the main antagonists trying to either kill him or use his power against his will. Another possible antagonist could be a powerful demigod who is jealous of Percy's new - found status and wants to take it for himself.
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.
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 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.
One possible plot could be Percy's discovery of his true parentage as the son of Kronos and Rhea. This could lead to a huge power struggle within the demigod world. Other gods and demigods might fear his potential power and try to either eliminate him or recruit him to their side.
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.