Well, one possibility could be that Naruto inherits some of Esdeath's cold and calculating nature. Maybe he uses her strategic mind to outwit his enemies in the Naruto universe. He could also have some unique abilities related to ice, like Esdeath does.
The Akatsuki could still be major antagonists. Their goals of collecting the tailed beasts would put them in direct conflict with Naruto, especially if he has the added power from his relation to Esdeath. They might see him as an even greater threat.
If Naruto is Esdeath's brother in fanfiction, they could embark on adventures across different dimensions. Since Naruto has experience with his own world and Esdeath with hers, they could explore new lands together. They might encounter strange creatures and powerful enemies. Along the way, they could learn from each other's fighting styles and abilities, Naruto teaching Esdeath about chakra and she teaching him about her own brand of combat techniques. And they could also be on a quest to reunite their fragmented family or uncover a long - hidden family secret that has the power to change their worlds.
The plot might involve Naruto having to deal with the stigma of being the'son' of Sasori. He could struggle to find his place in the ninja world while also having to face the enemies that Sasori made in his past. And he might use the skills he learned from Sasori in unexpected ways to protect his friends and the village.
The plot might revolve around Naruto being ostracized because of his relation to the 'son of scar' title. He then has to prove himself not only as a ninja but also to overcome the stigma associated with this identity. This could lead to many adventures where he battles against those who misjudge him and in the process, uncovers the truth behind the scar and his heritage.
Well, it could be about Naruto growing up in the Hyuga clan. Maybe he discovers his true parentage early on and has to deal with the expectations and politics of the clan. He might learn the Gentle Fist technique in a different way than Neji or Hinata.
Well, it could be about Naruto having some of Azula's traits. Maybe he has her strategic mind. For example, in battles, he could use her style of planning and outwitting opponents. And perhaps he has some of her fire - bending - like abilities translated into his ninja skills, like really powerful and precise fire - style jutsu.
Well, it could be about Naruto having some special powers or a connection to Ra due to being his 'son' in this fanfiction. Maybe he has to face new enemies or challenges related to this new identity.
Well, it could be about Naruto having some unique powers inherited from being the son of Medusa. Maybe he can turn people to stone with his gaze like Medusa. And his ninja skills combined with these new powers could make him an even more formidable fighter in the Naruto universe.
In a 'naruto son of gohan fanfiction', perhaps Naruto is born with a special power that is a combination of his own ninja abilities and some latent power from being related to Gohan. This could lead to him being an outcast at first in the ninja world as his powers are so different. But as he grows, he learns to master them and use them to protect his village and the world from new threats.
In a 'naruto son of asuma fanfiction', perhaps the story focuses on how Naruto's relationship with Asuma affects his relationships with other characters. For example, his bond with Shikamaru could be even deeper since Asuma was Shikamaru's mentor. And Naruto might inherit some of Asuma's fighting styles and philosophies, which would change the way he approaches battles and his ninja way.