No. In the official 'Dragon Ball' story, Vegeta is Trunks' father. Fanfiction might play with the idea for creative or alternate universe purposes, but it goes against the original lore.
One pairing that pops up is Goku and Chi - Chi. Their relationship as husband and wife can be explored further in fanfiction, especially in scenarios where Goku's Saiyan nature clashes with his family responsibilities. Additionally, Trunks and Future Mai is a pairing that has some popularity. Their relationship in the future timeline and how they support each other can be the focus of some great stories.
In fanfiction, one interesting aspect could be their different power levels. Goku is known for his Saiyan strength and his ability to reach new forms like Super Saiyan. Trunks, on the other hand, has his own unique fighting style. Fanfiction might explore how they train together, with Goku perhaps teaching Trunks some of his more advanced techniques. This could lead to Trunks achieving new levels of power as well.
Fanfiction authors often like to experiment with different 'what - if' scenarios. Making Goku Trunks' father could be a way to explore how the story would unfold differently. Maybe they want to see how Goku's influence would shape Trunks' personality in a way that's different from how Vegeta does. It could also be a way to merge different story arcs or character traits that don't usually interact in the original series. For example, combining Goku's pure - hearted nature with Trunks' more serious and future - focused attitude. This can lead to a whole new set of adventures and character developments that are not possible in the official story.
Their team - up also benefits from their shared Saiyan heritage. They can understand each other's drive for power and the importance of protecting their loved ones. This common ground allows them to communicate effectively during battles. For instance, they might use a combination of Goku's instant transmission and Trunks' swordsmanship to surprise their enemies.
In a fanfiction, there could be a scenario where an ancient prophecy foretells of a combined power of Trunks and Goku being the only thing that can stop an impending doom. They start training together to master a special fusion technique that no one has ever attempted before. Along the way, they face challenges not only in their training but also in dealing with their own egos and differences in fighting styles.
Zamasu is often paired with Goku Black. Since they are closely related in the original story, fanfiction writers like to explore their relationship further. It could be about their shared goals or how they interact on a more personal level.
One interesting fanfiction could be about Goku and Black Goku teaming up against an even greater threat from another universe. In this story, they might initially be at odds but gradually learn to work together, using their unique abilities to save the multiverse.
In fanfiction about Goku and Goku Black, a common concept is the alteration of their power levels. Writers may give Goku new forms or boost Goku Black's abilities in unexpected ways. There can be stories centered around Goku Black's adaptation to the main timeline's culture and society. For example, he might have to deal with the everyday life in addition to his evil plans. And there are fanfictions that focus on the psychological impact of their battles on each other, like how Goku might be affected by constantly facing an evil version of himself.
A Goku and Goku Black fusion in fanfiction could be really exciting. The fusion would inherit Goku's love for fighting and getting stronger, but also Goku Black's ambition. Their combined ki could be a new type of energy that no one has ever seen before. This new fused form might also have new transformations or abilities. For example, it could combine Goku's Super Saiyan forms with Goku Black's Rose form in unexpected ways. It could change the power balance in the Dragon Ball world and open up all sorts of new storylines, like teaming up with other characters to take on new threats or even having internal struggles between the two personalities within the fusion.