First, do your research on each of the source materials. Know the power levels, the personalities of the characters in Naruto, Gilgamesh's lore, and the world - building of DxD. Then, come up with a unique concept that can blend these three elements together. For example, you could have a crossover where a Naruto character is transported to the DxD world and meets Gilgamesh there.
One great Naruto, Gilgamesh and DxD fanfiction is 'The Convergence'. It has an interesting plot where the main character from Naruto somehow gets involved in the world of DxD and encounters Gilgamesh. The story is well - written with great character interactions.
He would likely be portrayed as arrogant. Given his status as a powerful and ancient figure in his original lore, in DxD fanfiction he would probably look down on most of the characters. He would act as if he is above the petty squabbles of the DxD world.
His personality would be a mix of pride and a sense of superiority. He'd walk around the school as if he owns the place. However, he might also have a sense of honor. For example, if he made a promise to a character in the DxD world, he would keep it, but in his own haughty way. He might also be somewhat dismissive of the school's rules, believing that he is above them.
One possible plot is that Gilgamesh views the High School DxD setting as beneath him at first. But as he gets to know the characters like Issei and Rias, he starts to see the value in their struggles. He could then use his vast resources and power to help them in their fight against stronger enemies, all while maintaining his haughty and kingly demeanor.
Maybe Gilgamesh gets involved in the power struggles within the DxD universe. He might see the different factions as beneath him but still decides to meddle for his own amusement. He could try to reshape the power structure according to his own ideals, which would lead to many interesting confrontations.
In Gilgamesh Highschool DxD fanfiction, there might be concepts like Gilgamesh forming alliances or rivalries with the devils, angels, and fallen angels in the Highschool DxD world. His vast treasures from his own story could also play a role, perhaps being used as bargaining chips or powerful weapons in the battles that often occur in the Highschool DxD setting.
The devils who oppose Gilgamesh's presence in the Highschool DxD world could be main antagonists. They might see him as a threat to their power and influence in the school.
Yes, there are likely some fanfictions out there with this concept. Fanfiction writers often come up with unique crossovers, and the idea of Naruto being related to King Gilgamesh in a fan - created story is not unheard of. You can try searching on popular fanfiction websites like Archive of Our Own or FanFiction.net.
He might become more confident, bordering on over - confident like Gilgamesh. Naruto is already confident, but with Gilgamesh as his father, he could have an even greater sense of self - importance.