Well, one possibility could be that Naruto and his mom gain mutant powers that are related to their chakra in some way. For example, Naruto might have a mutant power that enhances his already strong ability to use chakra, like being able to create chakra constructs more easily. His mom could have a mutant power that allows her to sense danger related to chakra imbalances. Maybe they have to hide their mutant nature in the ninja world at first because it's seen as something strange and different from the normal ninja abilities.
In a fanfiction where they are mutants, their relationship could be centered around exploring and understanding their powers. Naruto's mom could share her experiences of discovering and controlling her mutant powers with Naruto. They might develop a unique form of communication based on their mutant powers. Their relationship could also be a source of strength for Naruto, especially if he faces discrimination or fear from others in the village because of his mutant nature. His mom would be there to support him, and they would fight together to prove that mutants can be just as good, if not better, than normal ninjas.
One consequence could be a change in the family dynamic. His mom would be back, and Naruto would finally have the family he always dreamed of. This might also have an impact on his relationship with his dad, as they would all be together again.
One possible plot is that Naruto's lack of his mother's memory affects his ability to form relationships. He may be more hesitant to trust others, especially women, thinking that they might abandon him like his mother did (in his view of being forgotten). This could lead to some interesting character development, like him slowly learning to open up through his interactions with characters like Tsunade, who could act as a mother figure in a way, and through these experiences, he gradually pieces together his mother's story.
One possible plot could be Naruto getting to spend a day with his mom and dad in a special genjutsu - created realm. They could teach him new jutsu and share family stories he never knew.
In such a fanfiction, Naruto might grow up feeling extremely lonely and having trust issues. He could become more self - reliant, forging his own path without any family support. Maybe he would be more eager to prove himself to the village, not just to gain their acceptance but also to show his absent family what they missed out on.
One possible plot could be that a powerful and secret organization kidnaps Naruto as a baby right from his parents' arms. They might have some dark motives like using Naruto's potential power for their own evil schemes. Maybe they plan to raise him in a way that turns him against the Hidden Leaf Village in the future.
If such a fanfiction exists, a possible motive could be some kind of mind - control. Maybe an enemy uses a powerful genjutsu on Naruto, causing him to lose his sense of self and attack his mom. But this is still a very far - fetched and unethical concept within the Naruto world.
His training would likely be more intense. Since Kyuubi is a very powerful being, she would push Naruto to his limits. For instance, she might teach him more advanced chakra control techniques earlier than in the original story.
One possible plot is that Arin's mom was kidnapped because she had some special knowledge or item that a villain wanted. Naruto discovers this and tracks down the villain's lair. Along the way, he meets some old friends or makes new allies who help him. When he reaches the lair, he has to fight through a bunch of guards and minions. He uses his ninja skills and his quick thinking to outwit them. Once he finds Arin's mom, he has to deal with the main villain. He might use a combination of his Rasengan and his newfound friends' abilities to defeat the villain and save her.
Well, first of all, the backstory would need to be completely re - written. Haku would have to have some sort of relationship with Minato or some other way to be Naruto's mother. The fanfiction could focus on how Naruto discovers his mother's true identity. It might also show a different side of the Hidden Mist Village, as Haku is from there. And Naruto's personality might be influenced by Haku's more reserved and determined nature, leading to a different dynamic with his friends and enemies.