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.
The Akatsuki is also a possibility. They are after jinchuriki, and if they knew about Naruto's existence as a baby, they might try to kidnap him early. They could think that by having him from the start, they can better control the Nine - Tailed Fox within him.
Perhaps in this fanfiction, there is a prophecy about Naruto. Some people might believe that Naruto will bring great change, either good or bad, to the ninja world. Those who want to prevent the 'bad' change or those who want to accelerate the 'good' change might kidnap him from his parents. They think they can influence Naruto's upbringing and future actions according to their own desires.
Naruto might become more distrustful. Being kidnapped from his parents at a young age could make him question the intentions of others. He may grow up being more cautious around people and not easily trust those who seem friendly at first sight.
He could be using basic chakra control techniques to suppress his power. By constantly regulating the flow of his chakra, he can keep his true power hidden. For example, he might be using a form of internal chakra suppression similar to what some ninja use to hide their presence.
Another possibility is that Naruto has his own plans and goals that he wants to achieve independently. His true power might be a key factor in these plans, and he doesn't want his parents' influence or interference. He wants to prove himself on his own terms, without relying on his family connection.
Emotionally, Naruto would have to deal with a whole new set of family relationships. He grew up without his parents, and now having them back would be a huge adjustment. He might struggle to fit into a 'normal' family dynamic, and there could be some friction as they all get to know each other again.
In some fanfictions, Naruto might find a super - powerful jutsu or artifact. For example, he could discover a long - lost forbidden jutsu that has the power to bring the dead back to life. Or perhaps he stumbles upon a magical item during one of his adventures that is said to be able to revive the deceased.
On a personal level, Naruto would finally get the family he always wanted. But it might also bring some confusion and adjustment issues. His parents would be from a different time, and they'd need to adapt to the new world Naruto lives in. For example, they might be shocked by the new technology and the changes in ninja warfare.
Perhaps Naruto's parents were cursed or had some sort of premonition about a great danger coming to Naruto if he stayed with them. They believed that by separating from him, he would have a better chance of survival. Fanfiction writers often explore these kinds of emotional and complex scenarios to give a different perspective on Naruto's origin.