If you are a convicted felon, you are a "prohibited person" as regards firearms under Federal law. As such, you cannot touch a firearm, still less go hunting with one.
You may wish to review your case with a criminal defense attorney to confirm your status and ascertain whether you may have a means of having your conviction overturned. Your state and local bar associations can assist you with referrals.
No. NJSA 2C:39-7 makes it illegal for a person convicted of possession of CDS to possess a firearm. However, you are likely eligible for an expungement if you have no other criminal convictions. If you would like more information or assistance with expunging your conviction, please contact me.
NJ also has a Statute precluding a convicted felon from possessing a firearm, 2C:58-3. However you are eligible for a expungement 2C:52-1 et seq. State v. King 340 N.J. Super. 390 then allows possession of a firearm. I would utilize an attorney to expunge your record in this circumstance and perhaps raise the issue directly in the petition. The procedure can take as little as 8 weeks to complete but realistically it takes at least twice as long to get all the agencies to erase the computer records and lock up all the files. Call for a free consultation 908-687-6650.
You are going to need to consult with an attorney to determine if you are eligible for an expungement. Unless your conviction is expunged, you will remain ineligible.