Yes, there are quite a few. You can start by looking on fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Dragon Ball Goku's sister' and you'll find a variety of stories, some focusing on her training, others on her relationship with Goku and the rest of the Dragon Ball gang.
Another theme is the discovery of new powers. When Goku and Broly's sister interact, they might unlock new abilities within themselves. For example, through their combined energy, they could create a new form of attack or defense. This theme of growth and discovery is quite prevalent in such fanfictions.
One common theme is the exploration of forbidden love. Since Vegeta's sister and Goku are from different sides in a way, their relationship goes against the norm. Another theme is the power - up journey. They often train together and become stronger while dealing with their feelings.
One common theme is her struggle for identity. Since Goku is so well - known, she often has to find her own place in the world. Another is family bonds, showing how she relates to Goku and their other family members.
In the fanfiction, Goku might be initially shocked to meet his sister. He could then start to feel a strong sense of protectiveness towards her. Maybe they would train together to become stronger.
Common themes in 'Dragon Ball Goku's sister' fanfiction include the exploration of her place in the Dragon Ball world. This could mean how she fits into the existing power hierarchy. Another theme is her relationship with the other Z - Fighters. Some fanfictions might show her having a romantic relationship with one of them, which adds an interesting dynamic. Additionally, there's often a theme of self - discovery. As she discovers her powers and her role in the universe, she grows as a character. Some fanfictions also play with the idea of her having a different heritage or origin that ties into the overall Dragon Ball lore, which can lead to some really creative and unique storylines.
The plot could start with Vegeta's sister being sent on a mission to Earth. Goku, being the protector of Earth, initially sees her as a threat. But as they interact more, they realize they have a lot in common. They start to explore their feelings for each other secretly. However, Vegeta discovers their relationship and is furious. He challenges Goku to a fight, thinking Goku has betrayed him. In the end, Goku and Vegeta's sister have to prove to Vegeta that their love is real and that it won't harm their relationship as comrades.
One popular 'Goku x Broly sister' fanfiction might be 'The Unlikely Bond'. It explores how Goku and Broly's sister could form a connection in a unique and unexpected way, perhaps starting from a chance encounter during a battle on a new planet.