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.
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 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.
One scenario could be that Goku surprises Beerus with his speed and initial attacks as SSJ4. But then Beerus counters with his hakai and forces Goku to dodge constantly. Another could be that Beerus underestimates Goku at first and Goku manages to land some powerful blows.
Well, in many fanfictions, SSJ4 Goku is often depicted as having a chance against Beerus. SSJ4 Goku has shown incredible strength and combat skills. But Beerus has the power of a God of Destruction. His hakai ability could potentially wipe Goku out. Still, if the fanfiction is written in a way that gives Goku some new power - up or a special advantage, he could win. It really depends on the creative direction of the fanfic writer.
In many fanfictions, Vegeta starts as an outsider. He's a Saiyan in a world full of mages. His initial development is about adapting. He has to learn the rules of the Fairy Tail world. For instance, he might not understand the concept of magic guilds at first. As he spends more time there, he becomes more open - minded. He starts to see the value in the friendships and teamwork that are so important in Fairy Tail.
Goku is almost always a main character. His journey to master or use the SSJ4 form in new and exciting ways is a common theme. Vegeta is also often included, especially when it comes to rivalries and his own pursuit of power in the form of SSJ4. Sometimes, other Saiyans like Trunks or Goten might also be featured, especially if the story involves the next generation of Saiyans and their relationship with the SSJ4 transformation.
Another option is Wattpad. There are many Dragon Ball Super fans on Wattpad who write 'db super oc ssj rose fanfiction'. You might have to do a bit more digging through the search results, but it's possible to find some unique and engaging stories there.