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.
In 'oc son of goku fanfiction', antagonists can also be from other universes. There could be powerful warriors from parallel universes who come to challenge the OC because they see him as a key to controlling the multiverse or because they want to prove their universe's warriors are stronger. Also, some of Goku's old enemies might have descendants who hold grudges and target the OC as a way to settle old scores.
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.
The theme of femininity in the context of a powerful warrior like Goku is also quite common. Some fanfictions might explore how a female Goku balances her strength with traditional feminine qualities or how she defies the expectations of what a female Saiyan should be like. Also, there could be themes related to love and romance, especially in relation to characters she has a connection with in the original series, but with a new twist due to her being female.
I'm not aware of any such fanfiction. The relationship between Grandpa Gohan and Son Goku in the original story is one of love and mentorship, so this kind of dark and negative portrayal in fanfiction is not common that I know of.
In some 'oc son of goku fanfiction', a common plot is the OC's struggle with his identity. He is the son of Goku, a great hero, but he wants to make a name for himself. So he might embark on a quest to find a new form or a new fighting style that is all his own. Also, there could be a plot where he has to deal with the jealousy of other Saiyans who feel he gets special treatment due to his father.
One popular 'ash son of goku fanfiction' story could be one where Ash inherits Goku's Saiyan powers and uses them to battle in the Pokémon world. For example, he might use Super Saiyan strength to overpower really tough Pokémon or trainers.
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.