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Berberis thunbergii
You can generally distinguish barberry species by the number of branch spines (i.e., usually 1 or 3 spines at each node). I see a single spine at each location which is indicative of Japanese Barberry. However, if you have 3 at each node, it is B. vulgaris. If there is any variation in the number of spines, then you may have a hybrid.