Both of these expressions are USED nowadays (not 'using' - this is a passive construction, so you need the past participle.)
It's not your problem.
It's not your business or It's none of your business.
However, the expressions serve completely different functions. Please don't think that they are interchangeable.
'It's not your problem' is a relatively kind and polite response to make. If you have a problem and someone else offers to help, you could answer 'It's OK, don't worry, It's not your problem'.
By contrast, 'It's not your business' or 'It's none of your business' are both rude responses - similar to 'Mind your own business'. All of these mean 'Go away, this has nothing to do with you'. If someone asks an impertinent or impolite question, or tries to involve themselves in an affair which doesn't concern them, then someone might respond in this way. Use with care!