Yes, there are likely some 'naruto son of goku fanfic' out there. Fanfiction websites are full of creative and often crossover stories. You can try searching on popular fanfic platforms like FanFiction.net or Archive of Our Own. They have a vast collection of fan - created works, and with some keyword searching, you might find the 'naruto son of goku' fanfic you're looking for.
Well, it could start with some sort of interdimensional or magical event that links the Naruto and Dragon Ball universes. Maybe Goku somehow ends up in the Naruto world and has a relationship there, resulting in Naruto being his son. Then Naruto could inherit some of Goku's powers, like super strength or the ability to fly, on top of his own ninja skills. He might use these new powers to face even greater threats in the Naruto world, like stronger versions of the Akatsuki.
Well, it could be that Goku somehow ends up in the Naruto universe and has a son with a female character there. And this son has both the powers of a Saiyan like super strength and the ability to use chakra for jutsus. Maybe he's an outcast at first because of his strange powers but then becomes a hero.
Well, it could be about Naruto somehow obtaining the power of Son Goku. Maybe there's a strange jutsu that fuses their powers. Naruto could use Son Goku's strength in battles, like having his speed and ki blasts along with his own ninja skills.
A rogue ninja who has made a pact with dark forces. He wants to use Goku's son to open a portal to the Saiyan planet and then invade it. He would be constantly trying to manipulate the situation to get Goku's son to do his bidding. He has a team of minions who are also skilled in both ninjutsu and some dark form of ki - like powers.
It could be Orochimaru. He's always after power and seeing Naruto with Son Goku's power would make him a prime target. He might try to extract the power from Naruto for his own evil experiments.
It would be a really wild and interesting concept. Naruto's ninja world and the Dragon Ball universe of Goku Black are so different. Maybe Naruto would inherit some of Goku Black's powers like his ki manipulation. He could use it in unique ways in the ninja battles, like combining rasengan with ki blasts. And his personality might be a blend of Naruto's determination and Goku Black's more menacing side at times.
In a Goku Naruto crossover, both characters have their own strengths. Goku's physical strength and energy attacks are off the charts. His ability to instantly teleport and sense ki gives him an advantage in combat. Naruto, though, has a unique power system. His connection to the Nine - Tails and his ability to use different types of chakra make him a force to be reckoned with. If we consider a battle, Goku's power might seem greater on the surface. But Naruto has the advantage of being able to surprise his opponents with his ninjutsu and clones. Also, Naruto has a strong willpower that has allowed him to overcome many tough situations, which could play a role in a fight against Goku.
Vegeta from the Dragon Ball series is often popular. Fans like to write about his reaction to Naruto's world and how he might interact with the characters there. Also, Sasuke from Naruto is frequently included. He could be a rival or an ally in the fanfiction, given his complex character. Another one could be Piccolo. His calm and strategic mind would be interesting to incorporate in stories involving Naruto's more chaotic ninja world.