@Art
The leaves are very "finger-like".

@Pete
Yes, UCD has 2 Conadria figs; DFIC 05 and DFIC 50.
Not sure what the difference (if any?) is between them.
I only have a (back-traced) DFIC 05 specimen.

Gorgi, It has two leaf patterns, long finger like and one not so much.

Pete, Does your Conadria have a breba crop? This one has loads of breba.

http://figs4funforum.websitetoolbox.com/post/ripe-breba-pic-need-an-id-6412907

Art,
No breba crop this spring due to the 1 year old plants being out in 15 degree weather and frozen solid in their 5 gallon buckets this past winter, then pruned from a single stem to a potted tree form this spring. All the figs (about 6 dozen) this season formed on new growth. I may be able to answer your breba question next year, due to over 20 feet of new linear growth and possible breba formation on the tips.

BTW, I only had one or two leaves that had skinny finger like lobes early in the season.

Here's a link to one of the "more info" pages on the three (count 'em, three) versions of Conadria that Jon has listed in his Varieties pages.  
http://figs4fun.com/Info/Info_Conadria.html
A relevant quote from that page:  

Mike, You could be on to something.
As for fertilizing my trees, they surely weren't over fertilized this year. Just too many!
Here are some pictures of the plants in their first year. You can see the different leaves, especially in the third picture.

Art, am I missing something or is the history of this interesting fig more uncertain than you mentioned in this post: figs4funforum.websitetoolbox.com/post/vasilika-sika-stella-and-others-6583480
You said that the fig source thought it was from Italy? Wouldn't that make Conadria pretty unlikely? If it looks like a descendant of Adriatic (which Conadria is) maybe yours is also related but bred on the other side of the pond, so to speak. And if it was planted by an immegrant from years ago, what is the likelihood he planted a Conadria rather than a variety from the old country? Just my inexperienced 2 cents worth...I enjoy the histories and mysteries of these fig immegrants.
Hope you can find out more about it!

Excellent points Ed.  (And in addition to improbability of locale, does later than 1955 count as "years ago"?).  So Art, I'll second Ed's request to hear more about the history if it's possible to find out anything more.  (That's a fun part of it all, regardless of ID anyway).  

Ed, I've wondered also about whether similar crosses (to the one that Ira Condit did around 1955) have occurred spontaneously elsewhere.  Both of the parent figs (or ones very similar) for this cross might have existed around Italy for some time.  Maybe?

Mike

http://figs4fun.com/Info/Info_Conadria.html

The above link has some info on Conadria.  It is descended from Adriatic, an Italian variety, and a caprifig from California. Jon has some pictures of Conadria leaves under the 'more photos' tab.

Ed,  yep... that page was linked just four posts above yours (see post #31 in this thread).  It is good info, which Jon assembled from multiple sources (with attributions).  I also like the quote from it that says:  "Travellers (sic) remark on the big, juicy golden figs of southern Italy... Conadria brings those memories to life in your garden."  (The paragraph containing that line apparently came from Paradise Nursery, presumably back when Sybil and Rob ran it rather than current proprietors).  But lots of good info on that page.

Art, just to avoid obscuring the request above, I'll copy it again in this post so it isnt lost:  If you ever see a way to get more of the history of this one, it'd be interesting to hear.

Mike

Mike,  I visited Mr. and Mrs. Mittica today. I asked them about their tree and their reply was it was from Italy. They said that they and their relative in Pittsburgh are from Reggio Calabria. They believe that is where it is from. Their relative visits home often.

So, really it's all speculation. I will have to try to get in touch with the person in Pittsburgh.

Thanks Art.  (Hope I wasn't being pushy or putting you out asking for more info).  In any case, thanks for giving it a go.  It's all just kind of for the fun of it, so temper the amount of effort.  You've found a couple of good ones though, and with interesting good stories behind them.  (And who'd ever have thought you'd find great fig histories around Pittsburgh PA ??!!!).

Mike

Mike, Not pushy at all. I'm glad you are trying to help me out.
Here is another picture from a few minutes ago.
One thing I've noticed is that I've never seen any yellow with this variety. Pete said his Conadria turns a bit yellow before ripening. Have you noticed that?

I see mention of that in various writeups (the yellow upon ripening).  Nelson's pics look like maybe his turned a bit yellow too.  On mine, it was just the merest hint of yellow (this was my first year for fruit from Conadria and I only got two ripe figs), but there definitely was some yellow even if just a small amount.  I did see the color get noticeably lighter as it ripened though, just the boundary between light green and yellow gets kinda blurred.  I posted pics of my Conadria this year over in Nelson's thread earlier this month:  http://figs4funforum.websitetoolbox.com/post/conadria-6549147  (Pete has some photos of his there too, I think the same ones he posted above).  In the photos there it looks yellower than I remember it seeming to my eyes.

I'm still thinking along the lines that this could be a southern Italy (e.g. Calabria) variety that occurred naturally, possibly with parentage similar to the intentional cross that Condit and company did for Conadria.  Whether it has a name over there that's already established, tough to know.  I hear about lots of varieties from there that I've never seen, so who knows?  Whatever it is, it seems like an interesting fig.  That characteristic of good taste coupled with very good productivity (both breba and main crop), with a long period of near continual harvesting, sounds like good characteristics for small scale hobbyists like me.  The fact that it's got a story behind it that connects it with Calabria... well that just increases my interest.  :-)

Mike  central NY state, zone 5a

ConAdria - was bred by Ira Condit in California, USA.
The first 3 letters stand for his name.
The last 5 letters stand for an Adriatic fig he bred it from.

Well, I've got to throw an iron in the fire too.  Here are my leave photos of my Conadria which I obtained from Encanto Farms.  I can't beleive I didn't take one photo of my figs this year, especially since this was the tree that produced the most (6-7 figs).  I probably didn't take photos cause I was really disappointed in the flavor, or should I say lack thereof.  It was started March 2013 and resides in a 3 gallon nursery pot in full sun.  I remember this fig being light yellow in skin color and having a very slight red/amber flesh color.

Steve, That looks pretty similar. The only thing that my fig is lacking from the Conadria is the yellow.

Mike, You'll like this one. I think I have the exact same fig, but from another source.
I found this one about an hour away in another county. It also is sourced from Pittsburgh, Pa.

http://figs4funforum.websitetoolbox.com/post/anybody-recognize-these-leaves-6080370

I had one ripe fig from it this year and I think it is the same. I didn't take a picture. Wish I had.

More pictures. Does Conadria get the deep red that these get?

I don't know Art... none of the photos that I've seen of Conadria have that deep purplish outer pulp coloration  (I'm sure I haven't seen every Conadria photo though  :-)  ).  But given the full collection of info above in this thread, my thinking is that your Mittica White Unk is probably not actually a Conadria, but likely some naturally occurring cultivar from Italy that has parentage similar to the two figs that Condit crossed when he bred Conadria.  Whether it has some established name back in the old country or not, I don't know.  Anyway, that's what I'm thinking.  It sure does look like an interesting fig, whatever it is!  I'd suggest continue referring to it as Mittica White Unknown   (seems too many strikes against it being exactly a match for Conadria... the skin color upon ripening, the outer pulp coloration that you point out, and the timeline/story that (in order for it to be traceable to Conadria) would have to have had it brought from U.S. to Italy after 1956 or so, established there, and then brought back to U.S. by the family that traces it to you.  Also the leaf questions.).  Sure is a neat sounding fig though... the Mittica White Unkown!  You're starting to build up a set of these that you've found stories on, coming from Italy.  Very cool.

Mike   central NY state, zone 5a

I went back into my e-Bay "purchased list" and found that the Conadria cuttings I received from Encanto Farms were identified as "Late".  Maybe this might help us solve this mystery in the future.

Well here are the last few of my Mittica Unk. Picked today 12-11-13
These were ripened in my greenhouse. It was a high of 21 outside and tomorrow is only going to get to 17.
Surprisingly they weren't bad for a fig that ripened in horrible temps.

Any updates on this, or still going with Mittica Unk? Only reason I ask is I live due west of you in Ohio, so anything that performs well in our 6a zone is naturally going to acquire the attention of my fig obsession. 

These local unknowns are really cool, and it'd be nice to see them become official or something, established known cultivars maybe!

I am interested in hearing results on this fig from those that grow only in pots ..?