I have a New Jersey bank account and the New York State tax commission levied my account. Does NYState Tax commission have a right to levy my account without a New Jersey Warrant.

Most states that share a border have reciprocity agreements to allow the adjacent state to go after assets in the other state for legitimate past-due taxes.

I know that New York and New Jersey have such an agreement, so, yes, the levy by the NY state tax authorities is perfectly legal.