Dominic,
   Great question and one that as I give you an answer, you probably want to take a sample and a picture to your local full-season garden center/nursery and get a confirmation.
   When I first got the question, I opened the first picture and said to myself "this is a variety of fig." However, upon looking at the second picture of the tree itself, can't be. No fig has a common fruit tree shape and leaf structure.
   So, off I went to every resource I could think of to find a fruit, which is purple and egg shaped, grown in Ohio and could be ripening now.
   After all the research, it appears your tree is a plum tree. The variety I'm afraid, I would be just guessing and that's why I suggest a trip to your local garden center/nursery. There are varieties that somewhat fit what I see from your pictures.
   Now a few words in general about plums. First and foremost, plums ripen on the tree and are harvested as they ripen. When ripe, usually, just a soft twist and they will pop right off. They do not require a second tree to be pollinated - they are self pollinating. Plums are very hardy fruit trees and require a number of hours with temperatures below 32 degrees each winter to bear fruit. That number varies by cold hardiness and variety.
   Now the tricky part. Plums don't normally begin ripening in Ohio until mid-summer usually. I suspect this year yours got its required cold hours, but with the mild winter they blossomed early and are bearing fruit early.
   Your tree looks healthy and it is producing well. In fact, it looks like a bumper crop.
   Thanks for the question and I hope you have a great summer.