Given Naruto's Jinchuriki status, the child could have a special bond with the tailed beasts. Maybe not as a full - fledged Jinchuriki, but still be able to communicate and draw some power from them. From Koyuki, the child could inherit diplomatic skills. This would make the child a very interesting character, being able to handle both the power - based situations in the ninja world and also the diplomatic ones. And the child might develop a new form of ninjutsu that combines Naruto's Rasengan - like techniques with Koyuki's unique cultural jutsu.
One possibility is that the child has a unique form of sensory perception. Naruto has his own way of sensing things, and Koyuki might have some hidden senses related to her royal heritage. Combined, the child could have a super - sense that allows it to detect not only chakra but also other hidden energies or threats. Also, the child could have the ability to communicate with animals, a trait that could come from Naruto's connection to the toads and Koyuki's possible connection to the local fauna in her land.
The child could have Naruto's superhuman strength and stamina. After all, Naruto is known for his physical prowess. And from Temari, the child might inherit the ability to control wind chakra with great precision. So, they could be a force to be reckoned with in battles.
One possible reason could be Naruto's natural sense of justice. He can't stand to see a child in danger, and Koyuki being a child at that time, Naruto's heroic nature kicks in. He has always been the type to help those in need.
The child might inherit Naruto's powerful chakra reserves. With Naruto being a Jinchuriki, the child could have a large amount of chakra. Also, from Anko, the child could inherit her snake - related techniques or her stealth abilities.
The child could have the ability to combine Naruto's chakra - rich nature with Kurenai's genjutsu expertise. Maybe they can create a new type of genjutsu that is powered by a large amount of chakra, making it extremely difficult to break. This would give the child an edge in battles, as most opponents would not be prepared for such a powerful and unique genjutsu.
He could have enhanced physical strength and speed. Since he's raised as a weapon, his trainers would focus on maximizing his physical capabilities. Maybe he can move so fast that he's almost a blur in battle. And his strength could be on a level where he can break through solid rock walls with ease. Also, his chakra control might be more precise, allowing him to perform complex jutsu with greater efficiency.
Well, if Naruto and Yugito had a child in a fanfiction, the child might inherit Naruto's chakra reserves. Naruto has an enormous amount of chakra, which could be passed on. And from Yugito, the child could get the ability to control the Two - Tails. Their child might also be able to use some unique jutsu that combines Naruto's Rasengan - like techniques with Yugito's fire - based attacks related to the Two - Tails. Also, considering Naruto's strong will and Yugito's experience as a jinchuriki, the child could have great mental strength.
He could have a summon - like animal as a pet. For example, a toad that he befriends and keeps as a pet instead of just using for summons in battles.
The child could have a power related to the Hozuki clan's ability to turn into water. But with Naruto's genes, this transformation could be enhanced. For instance, they could transform into a larger body of water or be able to hold their water form for a longer time. And perhaps they could use the Nine - Tails' chakra to add a fiery element to their water jutsu, creating steam - based attacks.
Maybe the child has the power of mind control. Hermione is known for her strong mind and intelligence. Her child could inherit a more extreme version of this, being able to control the minds of others. This could be a very dangerous or useful power depending on how the child is raised and what their intentions are.
The story could be about the child inheriting Naruto's strong will and Koyuki's grace. Maybe the child would grow up in a world that is a mix of Naruto's Konoha and Koyuki's own land. The child might struggle with the expectations of being the offspring of two such important people and have to find their own path in the ninja world or in the diplomatic relations between the two regions.