I can't see the leaves in your photos, but most likely you have the Asian white mulberry (Morus alba). It's possible that you have the native red mulberry (Morus rubra), but unlikely. The white mulberry is everywhere and thrives in both urban and rural areas, spread by birds and squirrels and other animals alike. The fruits in your photo look like white mulberry. 

The fruit is edible on all mulberries, but I would discourage you from eating any fruit off the ground. Animals that carry diseases (raccoons, rats) may feed on and contaminate dropped fruit. 

I have been told that the slightly unripe fruit tastes better than the ripe fruit. Ripe fruit is overly sweet and lacking in flavor, in my opinion. You are welcome to try it and decide for yourself! 

If you decide that you do not like the fruit, you might consider removing the tree because of its tendency to reseed everywhere. It is not classified as invasive by the State of Michigan, but it is in many states (including Ohio).