For a zone 6b; after they have become mature, and planted in a protected location: Hardy Hartford, Hardy Chicago, Danny's Delight, Sal's EL, Blue Celeste, Sweet George, and Bayernfeige Violetta, and a few more. Check the old post on F4F.
For zone 6a through 5b: Marseilles Black VS, the new gold standard for cold hardiness. LaRadeks' English Brown Turkey, has endured lows of minus 18 degrees F. Hanc's English Brown Turkey, has been said it has been grown as far north as 4b, with winter protection.
But, keep in mind that fig trees cannot be grown like an apple or pear tree in these zones. They have to be protected the first 3 to 7 years, while the wood is becoming cold hardy.
But, if you want a trouble free fig for your zone, Marseilles Black VS is excellent.
Bob zone 5b - 6a Connecticut