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.
One interesting plot idea could be that Trunks and Goku have to team up to face a new, extremely powerful enemy from another dimension. This enemy has powers that neither of them has seen before, forcing them to quickly learn to combine their unique fighting styles. For example, Goku's Instant Transmission and Trunks' sword - fighting skills could be used in creative ways to counter the enemy's attacks.
Trunks could become Goku's mentor in some aspects. Since Trunks comes from a more technologically advanced future, he could teach Goku about advanced energy - manipulation techniques that are not yet known in Goku's time. This would create a new dynamic in their relationship as Goku looks up to Trunks in this particular area while still being the overall more experienced fighter in terms of raw combat.
It could be his father, Vegeta. Vegeta is known for his strict training methods and high expectations. If Trunks fails to meet those, Vegeta might punish him to make him stronger.
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.