After doing the "No one Escapes Cidhna Mine" quest all of the guards in Markarth constantly tell me they're going to take me to jail. I have the option to persuade them, but it doesn't work.
I ca also try and bribe but it doesn't work. I still have the option of telling them I've been framed that you get during the quest. When I say that they say they're going to take me to Cidhna Mine but I'm still in dialogue mode and all I can say is "I submit, take me to jail." When I say that the next dialogue option is "what's the problem?" and the whole conversation starts again.

If I press B to exit out of conversation the guards just talk to me again. It's stopping me from doing some quests since I can't talk to Calcelmo.

Any way to fix this?

load a previous save?

This may have accidently split into two posts you have to kill all the guards then enter then at the entrance inside there will be two more so I suggest you stock up on stuff for your health. There are two or three more people at the top of the stairs who come after you too but they're not guards and they can't be killed so avoid the top of the stairs because that's not where Calcelmo is anyway. Dogs will rat you out too. Don't be discouraged though because the mission is still pretty rewarding (though I'll leave that to you to find out)

I did the same mission and I don't know whether or not it's a glitch but you definitely can't go back to that prison. I completed that mission by killing all the guards. You're gonna have to 'cause it's not like you can sneak past them. Just make sure the fight isn't near Calcelmo 'cause he'll either run away in fear or try to fight you (though he can't be killed). If that happens exit and come back to him.

***Spoiler Alert*** As the mission says Calcelmo's a tough nut to crack so when the time comes to get into his mueseum and snatch his findings, just pick the lock or else you have to kill a spider (he'll give you more detail if you're persistent)