You have a couple of problems- being in NJ is one. The other is the felony conviction. No matter when- there is no time out for those. Also no such thing as a "minor" felony. It is or it ain't.
Under Federal law- (18 US Code, section 922) it is illegal for a convicted felon to possess a firearm. Penalty is 5 years, Federal prison, no probation or parole.
For persons that were convicted of a STATE felony, there IS a process to petition for restoration of gun rights. First step is to hire an attorney in YOUR state.
Persons convicted of a FEDERAL felony have no way to restore gun rights short of a Presidential Pardon.
IF you have not taken care of this, you will be denied a purchase permit, a carry permit, etc etc etc. And that is not just NJ.