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.
One possible storyline could be that Naruto is somehow transported to Goku Black's universe. There, he has to face Goku Black who sees him as an intruder. Naruto would have to quickly learn about Goku Black's powers and find a way to fight back using his ninja skills. Another storyline could be that a powerful villain creates a rift between their two universes and pits them against each other. They start off as enemies but then realize they are being manipulated and team up to fight the real villain.
There could be a storyline where Beerus, out of boredom, decides to train Goku Black instead of fighting him. But Goku Black misinterprets this as a sign of weakness and attacks Beerus. This could lead to a battle where Beerus has to hold back at first to avoid killing Goku Black, but as the fight progresses, he realizes he has to use his full power to subdue him.
One possible storyline could be that Goku Black arrives on Earth in search of a powerful energy source. The Justice League detects his arrival and confronts him. At first, they underestimate his power. Goku Black easily defeats some of the members, but then the League starts to work together and figure out his weaknesses. Another storyline could be that an evil entity has brought Goku Black to the DC Universe to cause chaos and the Justice League has to stop him while also dealing with the entity. Or perhaps Goku Black is tricked into thinking the Justice League are enemies of the Saiyans and he attacks them, only to later find out the truth and have to team up with them to fight a greater threat.
The different interpretations of the characters are great. In some fanfictions, Goku Black might be portrayed as even more evil or cunning than in the original series, and Hit could be shown with new strategies. For instance, a fanfiction might have Hit teaming up with other characters from different universes to take on Goku Black, which adds a whole new dimension to the story.
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.
There's also a fanfiction called 'Hit's Vengeance on Goku Black'. In this one, Hit is on a mission to avenge the destruction Goku Black has caused in the multiverse. It has some really intense fight scenes that are well - written. The author does a great job of portraying Hit's calculating nature and Goku Black's menacing presence.
One common theme is the clash of different power systems. Star has her magic from the 'Star vs the Forces of Evil' universe, and Goku Black has his Saiyan powers from Dragon Ball. Another theme could be the exploration of good and evil. Goku Black is a villain, so stories might focus on how Star and her friends deal with his malevolence. Also, the idea of interdimensional travel can be a theme, as Goku Black is from a different universe in Dragon Ball and would have to cross into Star's world.
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.