Sasuke could be a likely character in some fanfiction. Maybe in an alternate universe where their rivalry takes a darker turn, Sasuke might frame Naruto to gain an advantage or to prove his own superiority. It would add a whole new dimension to their relationship.
He could also rely on his own skills and past achievements. Naruto has saved the village multiple times. By bringing up these instances, he can show that he has always been on the side of good and that it doesn't make sense for him to be framed for something he didn't do. He might also use his ninja skills to investigate and find the real culprits, which would prove his innocence.
One possible motive could be jealousy. Maybe Naruto has achieved something that Sakura desires, like getting more recognition in the village. So, she decides to frame him to bring him down a notch.
One interesting idea could be the exploration of Naruto's character in a situation where he is wrongly accused and has to deal with the harsh prison environment. It might show his resilience and determination to prove his innocence.
I'm not sure specifically which ones are the most popular. However, in general, these types of fanfictions might explore dark themes such as Naruto being wrongly accused and then facing various forms of torture. They often deviate from the original positive and heroic narrative of the Naruto series.
One plot idea could be that Naruto is framed for stealing a powerful and ancient scroll from the village. The real culprit could be a rogue ninja who has the ability to disguise as others. Naruto then has to prove his innocence while on the run from the village's forces. Another idea is that he's framed for a crime that was actually committed by a corrupt member of the village council, who wants to get rid of Naruto because he's seen as a threat to their power.
Well, in the original Naruto storyline, Naruto is mainly focused on becoming Hokage and protecting the village from external threats. In the 'naruto framed prison fanfiction', he is suddenly in a position where he has to fight for his own freedom and reputation, which is a big deviation.
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.
It could also be a power play. In the Naruto universe, power is a big deal. Some might frame Naruto to get him out of the way in their pursuit of power. Since Sasuke has his own group of fans in the fic, they could be used as tools to achieve this by making it seem like Sasuke is against Naruto, when in fact it's all a setup.
In many such fanfictions, the development could involve Naruto's friends being initially misled by Sakura's framing. However, as the story progresses, Naruto's true nature and his past good deeds start to make some of them doubt Sakura's accusations. For example, Shikamaru, being the intelligent one, might start to suspect that something is off and begin to investigate on his own.