The most commonly used one is "third time's a charm". I googled it and couldn't find "three time's a charm" in usage. So is "three time's a charm" considered incorrect?
The correct expression is:
the third time is the charm
—used to say that two efforts at something have already failed but perhaps the third will be successful
I've never heard three time's a charm and I believe the inability to find any significant evidence of its usage is indicative.
According to The Phrase Finder:
the American expression 'third time's a charm' [...] may be an [sic] variant of the earlier 'third time lucky' or it may have arisen independently in the USA.