Under New York State law, ten years after your felony conviction, in addition to the time in jail or prison if any, one may submit a motion to seal the conviction. As an aside, in New York State, a felony conviction cannot be expunged.
If one is convicted of a felony and less than ten years have transpired from either the date of the conviction or if the sentence included incarceration, the date the person was released from jail or prison, then an Article 440 Petition could be made if there is a viable argument based on procedural grounds. In some cases, there are procedural irregularities in the plea-bargaining process, which could result in the plea being overruled. It is a long-shot but certainly the possibility must be explored.