How to find the number of citations for each version of an arXiv article?
A simple procedure would be to search for the arxiv identifier including the version number within articles citing the preprint in question. The arxiv identifier is explained here: Understanding the arXiv identifier.

Roughly as follows:


Find the article in a Google Scholar result list.
The entry usually has a link "Cited by: x". Follow this links to see the papers that cite the preprint in question.
It is now possible to limit further searches to the current result list. Do that and search for the arxiv identifier with version number added.


A quick example:

The paper arXiv:1207.1158 is cited roughly 609 times as of today: https://scholar.google.com/scholar?cites=4690497069002627251&amp;as_sdt=2005&amp;sciodt=0,5&amp;hl=de.

Searching for "arXiv:1207.1158v1" within the citing articles yields 4 results: https://scholar.google.com/scholar?q=arXiv%3A1207.1158v1&amp;btnG=&amp;hl=de&amp;as_sdt=2005&amp;sciodt=0%2C5&amp;cites=4690497069002627251&amp;scipsc=1, while searching for "arXiv:1207.1158v1" yields 6 results: https://scholar.google.com/scholar?q=arXiv%3A1207.1158v2&amp;btnG=&amp;hl=de&amp;as_sdt=2005&amp;sciodt=0%2C5&amp;cites=4690497069002627251&amp;scipsc=1.

As could be expected, the difficulty is that most papers don't include the arxiv identifier with the version number when citing an arxiv preprint.