The only time you should use “v.” as an abbreviation [for “versus”] is in legal contexts. In American law, the widely used citation standard is the Bluebook: A Uniform System of Citation, which demands that opposing legal parties be separated by “v.” when referring to a particular case. This usage is also used by the news media and other writers when referring to legal cases.
In other contexts, “vs.” (American English) or “vs” (British English) can be used as an abbreviation. This usage is more casual than writing out “versus.”