Naruto could use his chakra control to enhance his Kryptonian super speed. For instance, he could focus chakra on his legs while using his Kryptonian speed to move even faster and more stealthily. Also, his shadow clone jutsu could be combined with his Kryptonian powers. He could send clones with super strength or heat vision to attack enemies from different directions.
In a 'Naruto is Kryptonian' fanfiction, there are numerous possibilities. Naruto could have all the typical Kryptonian powers such as super strength, invulnerability, and super speed. This would completely change the power dynamics in the Naruto universe. For example, in battles, he wouldn't need to rely on shadow clones as much. His heat vision could be a substitute for some long - range attacks. Also, his origin story would be different. Instead of being an orphan because of the Nine - Tails attack, he could be an orphan because of Krypton's destruction. His relationships with other characters would also shift. His friends might be in awe of his new powers, and some might be jealous or even afraid. And the villains in the Naruto world would have to face a much more powerful opponent. There could be a whole new set of storylines revolving around Naruto's discovery of his Kryptonian heritage and how he uses it to shape the ninja world.
A common theme is power enhancement. Since Kryptonians have superpowers, when combined with Naruto's abilities, it creates a new level of power. Another theme could be cultural clash, as the Kryptonian and Naruto cultures are very different.
First, do your research on Kryptonian lore. Know their powers, culture, and history. Then, create an original character with unique traits within that framework. For example, your OC could have a different take on their Kryptonian powers. Next, think about how this character will interact with the Supergirl universe. Maybe they become an ally or a rival.
The story of Zod and the Kryptonian heritage is an epic one. Zod was born into a noble Kryptonian family. His upbringing instilled in him a sense of pride and duty towards his race. When Krypton faced its impending doom, Zod had a different plan than others. He believed that Kryptonians should be the dominant force in the universe. So, he set out on his own path. Along the way, he met other Kryptonians who had also survived the destruction. Together, they formed a small group. They traveled from planet to planet, spreading their Kryptonian culture and technology, while also facing opposition from some civilizations who feared their power. But Zod was not one to back down easily, and he continued to fight for what he believed was the rightful place of the Kryptonians in the cosmos.
One of the common themes is adaptation. A kryptonian in a new fictional world, say like the Star Trek universe, has to adapt to new technologies, cultures, and rules. They can't just rely on their Kryptonian powers all the time. Also, friendship and alliances are often themes. In a crossover with the Harry Potter world, a kryptonian might form alliances with the Hogwarts students to fight a common enemy. And of course, discovery is a theme too. Discovering new things about the crossed - over world and also about themselves as a kryptonian in a different context.
One popular kryptonian naruto fanfiction might be where Naruto somehow gets Kryptonian powers. For example, in some stories, he could be exposed to Kryptonian technology or meet a Kryptonian who imparts some of their abilities to him. This could lead to really interesting scenarios like Naruto being able to fly, having super strength, and still using his ninja skills in combination.
One great 'Supergirl OC Kryptonian' fanfiction is 'The Kryptonian's New Path'. It follows an original character who has unique Kryptonian abilities and their journey in the world of Supergirl. The story does a great job of exploring how this new character interacts with the existing Supergirl universe.
A big theme is also about acceptance. In many fanfictions, the hybrid has to face discrimination from both Saiyans and Kryptonians at first. For example, the Saiyans might see them as too soft because of the Kryptonian influence, while the Kryptonians might be wary of their Saiyan aggression. Overcoming this lack of acceptance and finding a place where they are respected is a common plot point. Also, the exploration of new powers that come from the combination of the two races is often seen. Their abilities can be unique and different from what either race has on its own, which makes for interesting storylines.
There's also 'The Hidden Kryptonian'. This one focuses on a female OC who discovers her Kryptonian heritage later in life. The author does a great job of showing her struggle to come to terms with it and how it changes her relationships. It's a story that keeps you hooked from start to finish.