I have done most of the TG city special quests.

trying to get the one for markath.

god dam it if delvin does not keep assigning me every city but markath. I try quitting job after job after job but am not getting markath. is there any mod that will force this idiot to give me something that will actually advance the plot?

Try getting a small job from Vex to see if it changes his 'mindset'.

Or simply leaving the cell and returning.

try getting both jobs from delving and vex. or you can do what they suggest in leaving and re-entering the area. it's just the luck of the draw, also, you can try to save before getting jobs. then if you don't get the job you need, restart the game.

Choose bedlam jobs there are only 5 of those available and try getting a job from vex

Have you completed the quest "The Forsworn Conspiracy/No One Escapes from Cidhna Mine?" Apparently it's extremely difficult to get enough Markarth jobs to get the special job there if you do those quests first. I had that problem on my first character, and it was the worst. On my current character, though, I made sure to do the special quest first and now I get Markarth jobs just as frequently.