Goku being born with SSJ4 in fanfic would likely make him a force to be reckoned with from infancy. This could result in quicker power-ups, different battles, and maybe even a shift in the balance of power among the characters.
One scenario could be that Goku surprises Beerus with his speed and initial attacks as SSJ4. But then Beerus counters with his hakai and forces Goku to dodge constantly. Another could be that Beerus underestimates Goku at first and Goku manages to land some powerful blows.
Well, in many fanfictions, SSJ4 Goku is often depicted as having a chance against Beerus. SSJ4 Goku has shown incredible strength and combat skills. But Beerus has the power of a God of Destruction. His hakai ability could potentially wipe Goku out. Still, if the fanfiction is written in a way that gives Goku some new power - up or a special advantage, he could win. It really depends on the creative direction of the fanfic writer.
Well, in Dragon Ball Super SSJ 4 Goku fanfics, his character development is often quite interesting. His SSJ 4 form is not just about physical power. He could start to understand the spiritual side of his power more deeply. He might go on a journey to find out the true origin of the SSJ 4 form, which leads him to ancient Saiyan or Namekian knowledge. This new knowledge could change his perspective on his role in the universe. He could also develop better leadership skills. Since he's so powerful in SSJ 4, others might look up to him more, and he has to learn to lead in battles and in making decisions that affect the whole group, not just himself.
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.
Well, his relationship with Vegeta would be interesting. If Goku went back in time and showed Vegeta the SSJ God form too early, Vegeta might become more competitive or even jealous earlier. He might push himself even harder to catch up, which could lead to more intense rivalries and also more joint training sessions between them.
One idea could be Goku traveling back in time to train with his past self. He could teach his younger self how to achieve the SSJ God form more quickly, which would change the power dynamics in his original timeline battles. For example, against Frieza, if he had the SSJ God power earlier, the fight would be much shorter and less arduous.
Well, I don't have a specific title off - hand. But a good place to start looking for 'Star vs the Forces of Evil Goku Black' fanfiction is Archive of Our Own. They have a wide range of fan - created works. You can filter by the relevant fandoms and look for stories that incorporate both elements in an interesting way, like maybe a story where Goku Black ends up in the dimension of 'Star vs the Forces of Evil' and causes chaos.
In some fanfics, a great plot twist is when Goku discovers a new, hidden power within his SSJ 4 form. This power could be related to his Saiyan heritage in a way that no one, not even Vegeta, knew about. Also, there might be a plot twist where the Dragon Balls are used in a completely different way. Instead of just wishing for power or bringing back the dead, they could be used to change the rules of the Saiyan power - up system, which would have a huge impact on Goku's SSJ 4 form.