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I am sorry to learn of this situation.
While you are required to pay child support for your own children, you are also entitled to visitation/parental rights for the child.
The New Jersey State Courts have a helpful guide to parenting rights - here: https://www.judiciary.state.nj.us/family/paretime.pdf.
You can enforce your rights in court (via a court order), but most parenting plans are created as a result of mediation - you do not need to have active litigation in order to reach a resolution. Contact your local (county) bar association and ask for referrals to mediators to assist you with this matter, often a third party neutral can assist you in reaching a mutually agreeable resolution.