I have found growing in my blueberry bushes several branches of what looks like the same leaf as the blueberry bushes, yet has small red oval berries on them. It seems like after I have cut a branch back, the next year this kind of branch grows back. Do you know what these are or why they come up in my bushes? They look like the wild bushes that I see growing along my wood line or in the woods. Will take over my blueberry bushes?
It most likely is growing from a the root stock.
Some Blueberry cultivators are grown onto root stock. This is most likely the plant you having growing up.
I would continue to prune it off as soon as it appears.