'Which president is Barack Obama in USA?' I would like to know whether or no the question tag `which' is correct in the above question.
To be grammatically correct you need to change "USA" to "the USA" as "the USA" is a proper noun that contains the definite article (it's just part of the name) and this isn't a context where you would drop it.
It remains unclear to me. I'm guessing that you mean "What position does Barack Obama have in the series of presidents of the USA?"
However, that confusion might be cultural on my part, as I'm from somewhere that doesn't count leaders as much, so it might be perfectly clear to an American. (Indeed, I've picked up that Obama is the 44th president by osmosis, but I couldn't tell you how many Taoisigh there'd been before Enda Kenny without checking, and I'm not even sure if I should call him the 13th or follow the American practice and call him the 20th due to non-consecutive terms counting separately).
But in terms of grammar the the is the only issue.