I never met his family and don't know where they are. What can I do?

Not a heck of a lot. You could ask for an exhumation. You can try to see if his DNA was recorded anywhere (police records, military service). You could try advertising for relatives.

But I'm not sure what establishing paternity will get you. You CAN list him on the birth certificate to give the child his name. But since he is deceased, there is no issue of support.

My son has his last name, but they can't put someone's name on a birth certificate unless they are there to sign. Also there is not a support issue but he could get social security death benefits. But thank you for responding

You're right Mattys_mom, there's the issue of SS benefits.

As Scott pointed out, you could try for an exhumation but I highly doubt they'll grant it.

Your best bet would be to locate his family - his parents or siblings would be able to take a DNA test to match for similarities between themselves, the deceased and your child.

Do you have any idea where they might be located? Did he ever mention any family or relatives? Mention where he grew up?