Honestly, it's a rather dark and niche area of fanfiction. One possible scenario in these fanfictions could be that Naruto is framed by a powerful and shadowy organization within the Naruto universe. They manage to manipulate evidence to make it seem like he's a threat. As for the torture, it could be in the form of being experimented on with some sort of forbidden jutsu, which is a very different take from the usual Naruto story where he's the hero saving the day.
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.
There could be many out there. Some might involve Naruto being framed by his enemies within the Hidden Leaf Village. For example, they could set him up to look like he's committed a serious crime against the village. Then, the torture part could be physical, like being put in a prison with harsh conditions, or mental, such as being isolated and having his friends turn against him because of the false accusations.
Chapter 391, ", Mr. Gu", is the clearest early answer because it turns Gu Hang's situation into a concrete plot event. The chapter gives readers a real answer by opening on During the call with Lois, the lady was quite surprised. and ending on Turning his head, he began to worry again..
Chapter 306, "The Benefits of Fighting for the Empire", is the clearest early answer because the buildup finally cashes out in a real clash. The chapter gives readers a real answer by opening on What are the benefits of fighting for the Empire as part of the Star... and ending on Even if all output went towards paying taxes, the excess Tax Currency....
Chapter 258, "Troops at the City Gates", is the clearest early answer because it pushes Knight Titan into a new phase or setting. The chapter gives readers a real answer by opening on Gu Hang and Wang Qi, this mother and son duo, discussed post-war... and ending on Through his military binoculars and the reports from his....
Chapter 361, ", Invading the Divine Realm", is the clearest early answer because Ge Wajia finally turns buildup into a real advancement. The chapter gives readers a real answer by opening on The Storm God Kingdom shook violently, and even Gu Hang in the real... and ending on Not to mention, the power of that incarnation was somehow used by....
Chapter 447, ", Iron Horse Naval Battle", is the clearest early answer because the buildup finally cashes out in a real clash. The setup is The small boat that had been following their trails didn't jump at..., but the pressure keeps building through It didn't matter if our boat was small, having many could do the job..
Chapter 409, ", Atonement Expedition, Independent Kingdom", is the clearest early answer because it turns Iron Armor Battle's situation into a concrete plot event. The setup is The grudge just keeps getting bigger., but the pressure keeps building through It had been some time since Cercis Flower was within the Princess.... Once the chapter lands on It wasn't about not being able to fight;
Chapter 821, "a major turning point", is the clearest early answer because it turns Ashen Dead's situation into a concrete plot event. The setup is Anconi Ben remained uneasy, but since things had come to this point,..., but the pressure keeps building through After all, from this assembly hall to the bridge command, it was at....
Chapter 255, ", The Liver and Gallbladder Fear the Cold", is the clearest early answer because it turns Luman Legion's situation into a concrete plot event. The chapter gives readers a real answer by opening on When Nes Luman and Gu Ming were so panicked that they didn't know... and ending on Their bombing target was the Luman Legion, which was interposed....
Chapter 338, ", A Hundred Thousand Favors", is the clearest early answer because it turns Rage Bear Legion's situation into a concrete plot event. The setup is These several changes directly reflected in the system conditions..., but the pressure keeps building through A few days ago, the option to annex finally appeared..
Chapter 428, ", I am the Dominant Bishop!", is the clearest early answer because it turns Warhound Titan's situation into a concrete plot event. The setup is In the span of over a year, she thrived on Jindi Star like a fish in..., but the pressure keeps building through The internal struggles within the Sect of Mechanics were quite....