I'm not entirely sure if there is a specific well - known fanfiction with that exact premise. But considering how fanfiction works, someone may have written a story like this. It could explore some really complex emotions and new storylines. Imagine Naruto growing up with Itachi's teachings and how that would shape his view of the ninja world, and also how the other characters would react to this new relationship. It would be a very different Naruto story for sure.
It would be a wild departure from the original story. Naruto's character would likely have a much more serious and calculating side, influenced by Itachi. His goals might be more in line with Itachi's own motives in the original series.
In this fanfiction scenario, Naruto meeting Itachi's son could be a very emotional encounter. Naruto, who had a complex relationship with Itachi, might see a lot of Itachi in his son. He could feel a sense of responsibility to guide the young boy. Maybe the son has some of Itachi's powerful abilities and Naruto has to help him control and use them properly.
If Naruto was Itachi's son in fanfiction, it would completely turn the story upside down. For one, Naruto's character arc would be different. His relationship with Sasuke would be more complex as Sasuke was Itachi's real brother. Naruto might have inherited some of Itachi's skills or traits. Also, the whole concept of Naruto being an orphan would change. Instead of being alone, he might have grown up with some knowledge of his Uchiha heritage, which could have led to a different path in his ninja training and his goals in the village.
In this fanfiction, Naruto's character would be a blend of his own exuberant self and Itachi's more solemn traits. He would be more perceptive, quickly understanding the motives of his enemies. His growth as a ninja would be faster in some aspects, like his ability to analyze battle situations due to Itachi's influence. He would also have a different relationship with the Uchiha clan. Since he's Itachi's son, they might see him as a symbol of hope or a link to Itachi's true intentions. This would all contribute to a more complex and multi - faceted Naruto character.
In this fanfiction concept, Naruto's powers would be a blend of his own and what he could inherit from Itachi. Since Itachi was a very powerful ninja, Naruto might have an innate ability for genjutsu, which was one of Itachi's strong suits. His chakra control could be improved due to his Uchiha blood. And with the Sharingan, he might be able to use Susanoo in the future, although it would probably be a different form compared to Itachi's, as Naruto also has the Nine - Tails' chakra. This combination of powers would make him an extremely formidable ninja.
There might be some very creative and out - of - the - box fanfictions out there that could have such a plot. However, it's quite an unusual crossover as 'Harry Potter' and 'Naruto' (where Itachi Uchiha is from) are two very different fictional universes. I haven't personally come across one, but with the vastness of the fanfiction world, it's possible.
The son might have a combination of Naruto's immense chakra reserves and Itachi's powerful Sharingan abilities. He could have the ability to use Rasengan with the precision and strategic thinking that comes from the Sharingan. Also, he might inherit Naruto's ability to learn new jutsu quickly and Itachi's calm and collected nature in battle.
Well, Naruto might be shocked at first. He'd probably notice the resemblance to Itachi right away. And then he'd start thinking about his own relationship with Itachi.
In such a fanfiction, the plot could involve Naruto growing up with Itachi as his father figure. He might inherit some of Itachi's unique abilities like the Sharingan in a unique way. Maybe he would face different challenges in the ninja world, as people would react differently to him being the son of Itachi. Also, his relationships with other characters like Sasuke would be very different, perhaps a more brotherly bond from the start.
Fanfiction.net is a great place to start. It has a large collection of 'Naruto Itachi Fanfiction'. You can search by popularity or by rating to find the ones that are most highly regarded. There are also filters to find completed stories or ones that are updated regularly.