I'm not sure which character you're referring to. Master Kai has a high chance of appearing in different novels and works because of this name. I will try my best to answer your questions if you can provide more context.
The show 'Cobra Kai' is indeed based on a true story in the sense that it takes the premise of 'The Karate Kid'. In real life, there are martial arts schools with different teaching philosophies, just like in the show. Cobra Kai represents a more aggressive and cut - throat approach, while other dojos might have more positive and harmonious teachings. The show then expands on this idea and shows how these different approaches can create long - lasting rivalries and how the characters grow and change over time as a result of their karate experiences.
One great 'Cobra Kai Fanfic' is 'The New Generation at Cobra Kai'. It focuses on the new students who join the dojo and how they adapt to the intense training environment. Another interesting one is 'Cobra Kai's Redemption Arc', which explores the possibility of some of the more antagonistic characters finding redemption. And 'Love in the Dojo' is a fanfic that delves into the romantic relationships that could potentially form among the characters in the Cobra Kai universe.
Cobra Kai is purely fictional. It takes the concepts and characters from the Karate Kid and builds on them in an imaginative way, rather than being rooted in real-life happenings.