A fanfic could explore their relationship through flashbacks. For example, Bardock could have left some sort of message or power for Goku that he discovers later. This would create an emotional connection between them even though they never really met in the original story.
One possible plot could be Bardock's adventures before Goku was born. Maybe it could show how he dealt with the Saiyan politics and his growing concerns about Frieza's rule. This could set the stage for Goku's future battles as his son.
One possible plot could be that Goku, having achieved new levels of power, somehow travels back in time to meet Bardock. Bardock, initially shocked, quickly realizes this is his son. They could have a sparring session where Bardock sees the full extent of Goku's power and is proud. Then they might sit and talk about Goku's life on Earth, and Bardock could share some of his own past battles and the reasons he sent Goku away.
For Goku, he could gain a deeper understanding of his heritage. Meeting Bardock would make him more aware of his Saiyan side. He might become more confident in his Saiyan abilities. For Bardock, seeing Goku all grown up and powerful could give him a sense of peace. He could realize that his sacrifice was worth it and be proud of the man his son has become.
One possible scenario could be an emotional reunion. Bardock, having seen Goku's future through his premonition ability, might be filled with pride. He could see how Goku has grown and the hero he has become in protecting the Earth. Another scenario could be Bardock arriving at a crucial moment during a battle Goku is in and lending his Saiyan strength to help Goku out. This would not only show their Saiyan connection but also the power of family unity in the Dragon Ball Z universe.
In a fanfiction where Future Gohan meets Goku, it could be an emotional reunion. Gohan might be filled with a sense of relief and joy, seeing his father again. He could show Goku all the things he's been through in the future, and Goku would be both proud and sad about what his son has endured.
It could lead to some really interesting plot twists. Maybe Goku could prevent major disasters before they happen and change the course of events in the Dragon Ball universe.
Bardock is a tough and battle - hardened Saiyan. When he meets Goku, who has a more pure - hearted and friendly personality, there could be an interesting contrast. Bardock might be initially skeptical of Goku's 'soft' ways but then come to respect his strength which comes from his good heart. Goku, on the other hand, would be curious about his father and would try to show Bardock the value of protecting others, not just for the sake of battle like the Saiyans usually do.
Goku's storyline would be affected in several ways. For one, without Vegeta, Goku might not have the same intense rival that pushed him to become stronger. Also, the Saiyan lore that Vegeta could have passed on to Goku would be lost. This could change Goku's understanding of his heritage and his place in the universe.