Some species of Rubus ie a bramble.

Rubus includes blackberry and dewberry, but a bird-seeded plant like that might or might not have appealing fruit even if it is technically edible. Its placement suggests it was planted by a bird who had eaten the fruit and then deposited the seed as it perched on your fence. ;>)

Agreed. Dig it up now and get rid of it before it makes fruit. The fruit isn't worth the plant taking over the place. It's awful.

Thank you all!! Agreed about getting rid of it. Although it may be "fun" to have berries in the backyard, I'm not crazy about it taking over the entire yard. Seems like round-up started killing it back pretty well. Once they grow a little more, I will dig all the baby plants up so they are just gone for good ... hopefully.

Thank you again!