I bought this tree a few years back. The guy told me he didn't know what it was called for sure but he said "I think it's a Brown Turkey." I knew it wasn't but didn't know what it really was. One year it grew but no figs. Same for the second. The third year it had about 8 figs but they all fell off by late August. This year I decided if I don't get a fig it's going in the compost pile. It had 5 figs, one fell off, one turned color without swelling in size. I touched it and it came off but the inside looked like it needed pollinated. Two swelled and fully ripened, one more to go. The ones that ripened were good, sweet with a slight melon flavor. It's a keeper as long as it ups the number of figs it can grow.
Hoping someone can help ID it. This one might be for Martin the dark fig expert to identify.

Looks like LSU Purple.

First thing I thought.

Ruben and Dom, thanks for your input. I researched LSU Purple and it certainly looks like it. Figs are like a box of chocolates, ya never know what you're gonna get. I was surprised what it really was. Good thing it produced an edible fig because I was going to pitch it this year. Close call for that tree.

Lol. Wahoo! Lucky, tony, I trashed my LSU died on me, way too dry, windy, and cold out here.