Can an illegitimate child receive settlement from a wrongful death lawsuit filed by a widow and her 2 children?

If the child can prove paternity, the child becomes a necessary party to the wrongful death action;  if you're the child and you have that proof, you need an attorney, to get you into the case and protect your interests.  There is no difference, under New Jersey law, between a child born in wedlock and one born outside a marriage, for purposes of inheritance or survivors' rights.

The problem, of course, is that if paternity hasn't already been established, it becomes very difficult to do that after the father's death.