Hi, Darwin
welcome to the forum! without the proper pictures, figs can be very difficult to identify properly (they can be difficult even with them!). What would help most is to have pictures of the whole ripe fruit, the halved fruit (lenghtwise), and the leaf shapes found after mid-season. If you can include a quarter or something of a commononly known size for reference would be helpful also. Your tree does sound delicious though and I'm sure many members would be intrested in trading or buying cuttings from you (myself included!). Once again, welcome!!