Yes, there are likely some fanfictions out there. You can try searching on popular fanfiction websites like FanFiction.net or Archive of Our Own. Just type in the relevant keywords and see what pops up.
Maybe Naruto, in his godlike form, ends up in the Dragon Ball Super universe and teams up with Goku to fight a common enemy. They combine their powers in unique ways to defeat the bad guy.
Well, a common concept is the crossover of characters' abilities. In some fanfictions, you might see Goku using Shadow Clone Jutsu to outnumber his opponents, just like Naruto does. Or Naruto might learn to sense ki instead of chakra. It's also interesting when the story explores the cultural differences between the two series. The shinobi way in Naruto and the Saiyan's warrior pride in Dragon Ball Super can create some great character - development moments when the characters interact. And, of course, there are always the epic battles that result from mixing such powerful characters and abilities.
Another aspect to consider is how the Super Saiyan transformation would affect the relationships in the Naruto world. If Sasuke were to gain Super Saiyan powers, it could either drive him further away from Naruto due to the newfound power or bring them closer as they explore the new abilities together. Also, the concept of ki from Dragon Ball and chakra in Naruto could be merged, creating a whole new type of energy for the characters to utilize.
A Super Saiyan in Naruto fanfiction could be a result of a dimensional rift. Maybe a portal opens between the Naruto and Dragon Ball universes and some Saiyan energy seeps through, affecting a Naruto character. This would be an interesting plot device as it would introduce an alien concept to the ninja world.
The pairing of Naruto and Goku is super popular. They both have a strong sense of justice and a love for fighting strong opponents. In fanfiction, they can often be seen training together or teaming up against a common enemy. Sasuke and Vegeta are also highly favored. Their quest for power and their complex personalities make for great story material. Additionally, some fans like the idea of Kakashi and Piccolo. Kakashi's intelligence and Piccolo's wisdom could lead to some interesting conversations and strategies in the crossover stories.
Character interactions are a big draw. Imagine Naruto and Goku becoming friends. Naruto could learn about Saiyan pride from Goku, and Goku could learn about the importance of teamwork from Naruto. Their different personalities would create really fun and dynamic relationships within the fanfic. Also, the clash of their different worlds' cultures, like the shinobi way in Naruto and the more straightforward fight - for - justice in Dragon Ball Super, adds depth to the story.
Well, it depends on how you define fanfiction. Technically, Dragon Ball Super is an official continuation of the Dragon Ball series. However, it does have elements that feel like fanfiction. For example, some of the power - levels and new forms introduced seem a bit outlandish and more like what a passionate fan might come up with rather than a strictly logical progression from the original story. But it's still an official part of the franchise so it's a bit of a gray area.
A cool fanfiction concept would be a tournament where characters from both Dragon Ball Super and Naruto universes participate. It would be exciting to see how Naruto's clones would fare against Goku's Instant Transmission or Vegeta's Galick Gun.
One interesting crossover could be a battle between Naruto's Rasengan and Goku's Kamehameha. It would be epic to see the different energy forms collide. Maybe Naruto could learn some of Goku's training techniques and vice versa, like Naruto trying to achieve Super Saiyan levels of power or Goku learning about chakra control.