Is your father living? if so, even if your parents never married, your dad’s income will be considered at some schools…usually the schools that give the best aid.
However, I don’t think any of the NJ publics use the dad’s info, and the state of NJ also gives aid when attending a NJ public.
If your father is deceased (sorry if that’s the case), then applying to schools that require NCP info will not be an issue, but you will have to provide your father’s death certificate.