How do I go about collecting money for my child after his father dies and he's not on the birth certficiate?

Do you have papers form the courts indicating that he is the father if not then most likely his mom will have to submit to a paternity test. At least that is how it happened with my
Cousin child.. he died before the baby was born. My aunt had to provide her DNA for the testing.

Yeah DNA testing is the only way to prove he was the father before you could begin to get anything.