Hello, I completed the Thieves Guild quest - "Arrow of Extrication". Then the "Independent Thievery" quest appears ant it says that I need to fence at least 800 gold. When I steal some goods from houses and go to Fathis Ules (best fence) location, and try to talk with him, he just says - "You've made your choice. Now leave me be." Then I go to any of the previous fences, I can sell goods to them. but the "Amount Fenced" is not increasing. I completed the "Sins of the Father" quest and gave the sword to Chorrol Count.
What should I do? Thanks in advance.

Once you handle that quest, Sins of the Father, the way you handled it, you can no longer work with Fathis. That's strange that none of the other fences will work... try again.... unless you've already fenced that amount. There is usually a wait, sometimes as much as a day (in-game) before I get the message that I've already fenced that much and am ready to move on.

If you're on the PC, get the unofficial patch. That takes care of the Fathis' not bartering issue. Also when bartering with the other fences, make sure the items you are selling have the red hand. It won't count unless the item is stolen. When you sell stolen items to them, there should be a number on the top left of the screen. You can also check your amount by talking to a Doyen and selecting the topic "special jobs" or something like that.

That's the problem! If I steal some items and try to sell them to fences - the red hand is not appearing!

I didn't reached the amount. My current amount is - 775 gold.