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.
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.
The relationship could develop in a more emotional way. Maybe Trunks gets injured badly in a fight, and Vegeta realizes how much he cares for his son. He then becomes more protective and affectionate towards Trunks. On the other hand, Trunks could also start to understand his father better, seeing that Vegeta's tough love is actually a way of showing his love and concern. This new understanding could lead to a more harmonious and loving relationship between them.
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.
Well, it could be about Goku Jr learning some of Goku's most powerful moves. Maybe Goku teaches him the Kamehameha. They might also go on an adventure together, like fighting a new and powerful enemy that neither could face alone.