Yes, in some fanfics, Naruto can be depicted as one of Orochimaru's experiments. Fanfic writers often like to explore unique and alternative storylines. They might imagine Orochimaru getting his hands on Naruto for various reasons, like to study the power of the Nine - Tails within him or to try and create a more powerful soldier. However, this is completely different from the original Naruto storyline.
One possible plotline could be Naruto being captured by Orochimaru and forced to endure various genetic experiments. Maybe Orochimaru is trying to extract the power of the Nine - Tails from Naruto in a more invasive way. Another could be that Naruto's friends, like Sasuke and Sakura, attempt a daring rescue mission while Naruto is in Orochimaru's clutches and they face off against Orochimaru's minions.
In a fanfic where Naruto is one of Orochimaru's experiments, it could completely change the trajectory of his life. First, his training under Jiraiya might be affected. Jiraiya might be more cautious or even hesitant to train him further. Naruto's own view of himself would also change. He might question his identity and purpose more deeply. His powers could be a mix of his original abilities and the modifications made by Orochimaru. This could lead to some really interesting battles where Naruto has to learn to control these new powers while still holding onto his values. And his interactions with the other characters, like Sasuke and Sakura, would be very different. Sasuke might see him as a more direct threat, and Sakura might be more worried about his well - being.
Well, the experiments might initially make Naruto question his own identity. He might wonder if he's still the same Naruto after all the changes Orochimaru has made to him. But in the long run, it could lead to a more mature Naruto. He might start to view his power and purpose in a new light. He could become more self - reliant, not just relying on the Nine - Tails' power but also on his own newfound abilities from the experiments, and use them for the greater good.
In some fanfics, Naruto might use his new and powerful jutsu that he has mastered over time. Maybe he combines his Sage Mode with the power of the Nine - Tails in a unique way that Orochimaru can't counter. For example, he could use the Nine - Tails' chakra to enhance the range and power of his Sage Mode attacks, and then catch Orochimaru off - guard.
One consequence could be a shift in the power balance among the ninja villages. Since Orochimaru was a powerful and feared figure, his death might cause some chaos as his former allies or subordinates try to either avenge him or claim his resources. For example, some of his secret labs and experiments might be up for grabs, leading to potential conflicts.
In fanfic, anything can be possible, so Orochimaru could be Naruto's father. But in the official Naruto storyline, it's not the case. Naruto's parentage is clearly defined as Minato and Kushina. Fanfic writers might be trying to explore a different kind of family drama or a new take on the characters' relationships by creating this unorthodox connection.
One possible fanfic could be about a student of Orochimaru who rebels against his evil ways. This student, perhaps having seen the destruction Orochimaru causes, decides to use the knowledge he has gained in a positive way. He might start by secretly helping the Hidden Leaf Village, using his skills in jutsu and forbidden arts to protect rather than harm.
In some fanfics, Orochimaru can be made Naruto's sensei. Fanfic authors often like to play with the original story's elements and create unique scenarios. They might think that having Orochimaru as Naruto's sensei would lead to a very different kind of character development for Naruto, full of more moral and ethical challenges due to Orochimaru's dark nature.
One possible scenario could be Naruto exploring new jutsu by experimenting on his own chakra. Maybe he tries to combine different elemental chakra within himself in unorthodox ways to create a super powerful and unique jutsu. Another could be related to his physical endurance. He might experiment with training methods that push his body to the limit, like enduring extreme pain or fasting for long periods while still trying to perform at his best in combat simulations.