In this situation, Naruto could also use his ninja skills in a discreet way. For example, he could use his shadow clone jutsu to gather information without being noticed. He might discover that the ones who framed him are actually part of a larger conspiracy against the Hidden Leaf Village. So, his main goal would then not only be to get out of prison but also to expose this conspiracy.
Another possibility is that some of his friends from the village would suspect that he was framed. They could start their own investigation on the outside. Sakura, for instance, might use her medical skills to analyze evidence that was overlooked. Meanwhile, Naruto inside the prison would have to endure the harsh conditions and deal with other prisoners who might be hostile towards him because of his reputation as a powerful ninja. But he would keep his spirit high, believing that one day he will be free and his name will be cleared.
He could use his transformation jutsu. He could transform into a guard or an inmate who has access to the prison exit areas. Then he could just walk out when the opportunity arises.
In fanfiction, if Naruto gets sent to Blood Prison, he might face a lot of challenges. He could encounter powerful and dangerous inmates. Naruto would probably try to use his ninja skills and his strong will to survive. Maybe he'd also find some allies among the prisoners who recognize his strength and good heart.
Well, Naruto would likely bring his sense of determination and never - give - up attitude to Earthland. In Earthland, which has its own set of power systems and magic, Naruto could start to learn and combine his ninja skills with local magic. He might form new friendships with local mages, and together they could face challenges that neither could have faced alone. For example, he could help in fighting against some dark guilds that are causing chaos in the land.
Another possibility is that his time - traveling could create some sort of time paradox. This might lead to all sorts of strange and unexpected consequences. His presence in the past could disrupt the normal flow of magic and time, and he'd have to find a way to fix it before everything goes wrong.
He might face some really tough opponents. In the Naruto world, Hozuki Castle is known for being a dangerous place. Naruto would probably use his signature jutsu like Rasengan to defend himself. Maybe he'd also try to make allies among the inmates there.
Well, in this type of fanfiction, Naruto could change the relationships he had at the academy. He may befriend Sasuke earlier and in a different way, perhaps preventing Sasuke from being so cold towards him initially. Also, he could have more time to train with his classmates and help them improve too, which would make for a very different dynamic in the group.
It could be that Naruto is sent to prison as part of a political move. There are some ninja clans within the village who are jealous of his popularity and influence. They conspire to get him out of the way by making it seem like he's a threat to the village's security. In prison, Naruto discovers a hidden conspiracy within the prison walls that is related to the outside political turmoil and he has to find a way to expose it while also getting himself released.
Well, Naruto might use his Nine - Tails chakra to break free. He's a tough one. He could also try to outwit Orochimaru with his ninja skills. Maybe he'd pretend to be unconscious and then surprise Orochimaru when he least expects it.
Well, he could be tortured for information about Konoha. The Iwa ninjas might try to extract secrets about new jutsus or strategic plans. They could also use him as a bargaining chip against Konoha.
Naruto could find a book that tells the story of a great hero who was just like him, full of energy and a desire to protect. This could inspire him to new heights. He might also accidentally trigger a trap or a hidden mechanism in the library while exploring, leading to an adventure filled with challenges and puzzles to solve.