The Shards of Mehrune’s Razor

You've likely hit a bug.

While you've agreed to help Sinding, it doesn't lock in your choice: if you attack him at any time before the end of the quest (when the curse is removed from the ring, allowing you to take it off), you lock in your choice to help Hircine.

However, doing so is supposed to go down differently: you act as one of the hunters and chase Hircine through the grotto, ending with you skinning him. He's not supposed to appear in jail.

You can try that: kill him in jail and skin him. If that part isn't bugged, Hircine should appear and complete the quest for you. As a reward, the ring will disappear.

Otherwise, welcome to a Bethesda game, where crippling bugs like this are par for the course in the first couple of weeks after launch.

The briar hearts in this quest are apparently prone to glitches. I found this thread where people are discussing the various ways in which they were able to break this quest. In some cases, when they got notification that they needed to get that specific briar heart, all the briar hearts they already had became quest items.

I think the best you can do is load an earlier save, or hang on to this quest until Bethesda patches it to work properly. Even so, you might not be able to finish it unless they create some way to reset your progress in it or otherwise fix the quest if it is already in progress.