In the 'Bardock Saves Raditz' fanfic, perhaps Bardock discovers a way to time - travel. He goes back to the moment when Raditz is about to die. Bardock could use his own power to shield Raditz from Goku's Kamehameha. Then, they team up and start exploring other planets, trying to find a new place for the Saiyans to thrive, away from Frieza's tyranny.
Perhaps the main antagonist could be a new character. This new character could be an ancient evil that has been awakened by the presence of the Saiyans on Earth. They see Bardock and Raditz as a threat to their plans of taking over the universe and thus try to eliminate them.
One idea could be to focus on Bardock's perspective before his fateful battle. Maybe explore his thoughts about his son Goku being sent to Earth and his own impending doom. He could have some premonitions about Goku's future role in saving the universe.
It could be a story of redemption for Raditz. He starts off as a bit of a villain, but through interactions with Bardock (either as a memory or some kind of spirit guidance) and Goku's influence, he changes his ways. They could all be training together on Planet Vegeta before its destruction, with Bardock teaching them valuable Saiyan combat techniques and life lessons that shape them into the characters we know.
I haven't read this particular fanfic directly, but generally, in a 'bardock saves broly' fanfic, it might involve Bardock using his combat skills and intuition. Bardock, being a Saiyan, has a certain level of power and tenacity. He could potentially save Broly from some sort of danger, like a powerful enemy or a life - threatening situation on their home planet. It could also explore the relationship between the two Saiyans, perhaps Bardock seeing potential in Broly or having a sense of kinship towards him.
Bardock's power could be shown as more raw and instinctive. Since he was a pure - blooded Saiyan from a time when Saiyans were more about brute force and conquering. Raditz might have a power level that is in between Bardock and Goku. His power could be more focused on intimidation at first, but as the fanfic progresses, he could develop it further. Goku's power, on the other hand, would be more about growth and adaptability. He learns from his battles and constantly improves, so his power could be shown as evolving more rapidly than the others.
One great 'Bardock Raditz Saga Earth Fanfic' could be about Bardock arriving on Earth earlier than expected. He might start to train some of the Earth's warriors secretly, changing the course of future battles. This would add an interesting twist to the Saiyan - Earth relationship.
Bardock may start as a typical Saiyan, focused mainly on fighting and power. But as he faces the threat to Planet Vegeta, he could start to develop a sense of responsibility. He realizes that there's more at stake than just his own glory in battle.
One interesting 'Bardock Raditz Saga' fanfic could be one that delves deeper into Bardock's premonition powers. It might explore how he got them and what other visions he could have had. Another could focus on Raditz's early life on Planet Vegeta before being sent to Earth. There are also fanfics that might rewrite the saga with different outcomes, like Bardock surviving and changing the course of Saiyan history.
First, research the existing lore of the Bardock and Raditz sagas. Know their personalities, powers, and backstories. Then, think about how their presence on Earth would change things. You can start with a simple plot idea, like Raditz teaming up with Goku against a new threat on Earth.