A 'naruto ssj3 fanfic' is likely a fan - made fictional story that combines elements of Naruto and the Super Saiyan 3 (SSJ3) concept from Dragon Ball. It could be about a Naruto character achieving a form similar to SSJ3, perhaps with new powers and abilities, and the adventures or battles that follow.
As I said before, without more context, it's hard to determine who exactly Andy King is in the story. He could be just an ordinary person with an interesting life experience.
You can try fan - fiction websites like FanFiction.net or Archive of Our Own. They usually have a wide variety of fan - created works, and there's a good chance you'll find 'naruto ssj3 fanfic' there.
Goku being born with SSJ4 in fanfic would likely make him a force to be reckoned with from infancy. This could result in quicker power-ups, different battles, and maybe even a shift in the balance of power among the characters.
One idea could be a crossover with the Naruto universe. Gohan as SSJ2 could end up in the Hidden Leaf Village and interact with the ninjas. Maybe he helps in a battle against a powerful enemy using his Saiyan powers.
One of Andy Liu's movies was Curse of the Dragon, which was released in 2002. It was directed by Director Li Rengang and starred Andy Liu, Zhou Yong, Zhang Jingchu, and others. The movie was an action movie about the ups and downs between good and evil.
One interesting story could be about a new villain who forces Goku to reach the SSJ4 form in a completely different way. Maybe he has to combine his Saiyan powers with some ancient energy source on a new planet. Another could be a fanfiction where Vegeta finally masters the SSJ4 form before Goku and has to face a powerful foe alone.
You could start by establishing the setting and the situation. Say you choose a crossover with the Avatar: The Last Airbender world. Begin with Gohan SSJ2 sensing an unusual energy in that world and deciding to investigate. This sets the stage for the story to unfold.