She would likely have incredible chakra reserves, inherited from both Naruto and the Kyuubi. This would give her the ability to perform powerful jutsu for long periods without getting tired easily. For example, she could use large - scale elemental jutsu like Naruto's Rasengan, but with even more strength.
Another possible ability is enhanced physical strength and speed. Naruto was already quite strong physically, and combined with the Kyuubi's influence, she could be even more formidable. She could move at blinding speeds and deliver powerful punches and kicks, making her a force to be reckoned with in close - combat situations.
She could have the ability to manipulate space - time like Kaguya. Maybe she can create portals or slow down time in a different way. It would be a natural extension of Kaguya's powers.
Naruto would likely be curious about her. He might approach her with his usual friendly and open - minded attitude. The daughter, depending on her personality, could be either shy or bold. If she's shy, Naruto would try to make her feel comfortable. If she's bold, they might start off with some friendly banter.
Naruto could gain the ability to manipulate fire in a unique way. Since the Kyuubi is associated with a certain element - like energy, it could translate into Naruto having a new form of elemental jutsu. He might also be able to heal faster. Kyuubi's chakra has shown to have regenerative properties, and with a bloodline, this could be enhanced in Naruto, allowing him to recover from injuries more quickly.
His chakra control would likely be extraordinary. Kyuubi is a huge source of chakra, so Naruto would have had early exposure to vast amounts of it. This could lead to him being able to perform more advanced jutsu at a younger age.
He would likely have some dark - based abilities. Maleficent has powers related to dark magic, so Naruto might be able to manipulate shadows or darkness in some way. For instance, he could use shadows to move around stealthily or create illusions within the shadows.
Naruto's character development would be quite a journey. Initially, he would be in denial about this new form. But as he realizes he can't change it easily, he starts to embrace it. He would learn new values from the Kyuubi's side, like the importance of being cunning in battle. His character would become more well - rounded. He would still have his old traits like his never - give - up attitude, but now he'd also have the Kyuubi's influence. For example, he might be more territorial when it comes to protecting the village, like a fox protecting its den. His character would evolve to fit this new role and the powers that come with it.
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.
It could be in an alternate universe fanfic where the rules of the Naruto world are completely rewritten and Naruto's identity as the kyuubi is central to a new and unique storyline.
Her relationship with Naruto could be very special. Since Naruto has the Kyuubi within him, he might feel a certain kinship with her. He could be like a father figure to her, guiding her and teaching her how to control her demon side. Naruto, having experienced discrimination himself, would be very protective of her and ensure that she doesn't face the same kind of mistreatment he did.
Another possible new ability is the power of astral projection. Jupiter has a connection to the celestial realm. Naruto, as his son, could project his spirit into the astral plane. This would give him the ability to gather information from afar, spy on enemies, or even communicate with other celestial beings. It would add a whole new dimension to his ninja skills, making him not just a physical fighter but also a spiritual one.