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The question is based on somewhat of a faulty premise. Y-DNA I did not emerge "in the Balkans during the Mesolithic." It certainly arose during the Paleolithic, we're not sure where, and had diversified into several branches (about 11 or so of which have been found extant today) by the beginning of the Mesolithic. Also, I'm unaware of any mtDNA haplogroups that arose in Europe, unless we're talking about subclades, at which point, the answer is "a lot." An easier question to answer is "what mtDNA haplogroups were in Europe by the beginning of the Mesolithic?"
To answer that: We know N* was for sure, and it appears that R0, HV, and U were as well, as that's what we have in terms of ancient Paleolithic samples so far. Certainly U5 became quite common during the Mesolithic, apparently eventually beating out N in terms of frequency. H, U4, V, K, and T have also been found in ancient Mesolithic DNA samples. We don't have any samples that I know of from the Balkans in particular, but I suspect that the pattern is similar there as with the rest of Europe.