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, Vegeta would be a likely character. He might be initially suspicious of the female Goku. Maybe he thinks she's a threat or just can't believe there's another Goku - like being. He could be there to add some comical moments as he tries to understand the situation.
In general, it's a bit of a toss-up. The strength of Manga Goku and Anime Goku can vary depending on the specific arcs and battles. Sometimes, it might seem like one is stronger in a particular situation, but that could change in another.
Another possible main character could be the villain that forces the two Gokus to meet. This villain could be a new, super - powerful threat that the two Gokus need to deal with. Their meeting becomes a crucial part of the story to defeat this powerful foe.
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.