Yes, there are quite a few. You can start by looking on fanfiction websites like Archive of Our Own. Some fanfictions might explore their relationship in different ways, like how Vegeta's tough exterior softens when it comes to his daughter Bulla. It could show him being protective, teaching her Saiyan ways, or just having cute father - daughter moments.
It could be a genetic mutation in the fanfic's storyline. Some strange event or factor could have caused a change in Bardock's genes, making it possible for him to become Super Saiyan. This genetic change might be related to some ancient Saiyan lore or a new element introduced in the fanfic's universe.
One common theme is protection. Vegeta, being a powerful Saiyan, will often be shown protecting Bulla from various threats. Another is teaching. He might teach her combat skills or about their Saiyan heritage. Also, there can be themes of family bonding, showing how Vegeta's love for Bulla strengthens the family unit.
One possible plot could be Vegeta training with baby Bulla. He could be teaching her the basics of combat in a gentle yet firm way. For example, showing her how to throw a proper punch or dodge an attack. He might also tell her stories about their Saiyan heritage during breaks in the training.
Well, if Naruto goes Super Saiyan 3 in a fanfiction, he would likely gain an insane amount of power. His physical abilities would skyrocket. He could move at incredible speeds, and his strength might be enough to shatter mountains. His chakra would probably combine with the Saiyan power in some unique way, creating new and powerful jutsu.
Well, in this fanfiction concept, Naruto going Super Saiyan 4 could also lead to some interesting character dynamics. His friends might be initially shocked and a bit scared of this new form. Naruto would then have to prove that he's still the same person despite this radical transformation. And as for the enemies, they would surely be caught off - guard and have to quickly come up with new strategies to deal with this super - powered Naruto.
Well, an interesting interaction could be when Vegeta first holds baby Bulla. His tough exterior softens as he looks at this tiny being. He might mutter something like 'You will be strong, little one.' Another could be when Bulla starts to cry and Vegeta tries to figure out what's wrong. He's used to dealing with battle situations, not a crying baby, so it's a bit of a comical yet heartwarming scene.