I have this vine growing in my yard in Northern Indiana but since there are three leaves I chose to just stay away from it. I would appreciate help in identifying these tempting berries


I am no expert, but it looks like a Dewberry to me. Dewberries look like blackberries but they don't always have the same conic shape and are smaller. Here's a link to a website with a few pictures: http://www.redhousegarden.com/2014/08/dewberries.html?m=1 . It's about the right time for dewberries to ripen too. Hope that helps!
Even though I don't see any thorns in your pictures, I'm pretty sure those are wild (or feral?) blackberries. Hate to tell a stranger, long-distance, that something is edible, but maybe you can convince yourself by smelling some crushed ones??? Or better yet, ask a neighbor to be sure.