There was a thread about this recently, within the last 6 months, but I cannot find it for the life of me.
In that thread, there was a discussion about JH Adriatic producing the first year (via Herman?). However, I do not know if the person reporting this was saying "first year the cutting was rooted" or "first year after rooting".
The thing is, most everyone knowledgable with fruiting vines, trees and bushes will tell you, you absolutely must remove all fruits from a sapling tree to prevent stunting its growth or outright killing it. Figs are, in my opinion and the opinion of others, no different in this regard.
I will remind you again (with a smile) - "patience is a virtue". You should probably wait until the first year after rooting before expecting fruit.
I can tell you from years and years of experience that the two hardest things that any grower has to do is 1) "thin out" their plants and vegetables to make room for the others to grow up big and strong, 2) remove branches or fruits from their plants and vegetables to allow them to grow up strong and produce the best quality product possible.
Every year when I sow seed in my vegetable garden, I deal with the pain of "thinning out" excess plants (basically killing 1/2 of my germinated seedlings) so that the other vegetables aren't too crowded to grow up. In my mind, I know it's the right thing to do, because I've seen how badly it hurts all of them to be crowded. In my heart, I feel like I should be doing something more to save them so I have twice as much of a crop! (I don't have the space to do that, though!)
Just the same, every year, I need to prune my fruit trees and bushes and pluck off flowers to make sure the tree or bush is big and strong enough to support the fruit which will grow on it, and make sure the branches are large enough to carry the right amount of nutrients to make the fruit the best possible piece of fruit it can be.
It's just part of the process!