I see that your name is on the birth certificate, but at any point did you sign something at the hospital called an "Acknowledgement of Paternity" or was there a petition filed with the court to establish custody? If so, you would already be considered the custodial parent since there is no other legal living parent. Have you tried showing the birth certificate, acknowledgment of paternity or paternity order along with a copy of the mother's death certificate? The bank should provide guidance on what you need to establish this. I see no other reason for them not providing access to your son's assets.
I'm presuming you signed the acknowledgement of paternity or there was a paternity order establishing you as the legal father or the state would have likely taken custody of the child to find the next of kin. If they haven't gotten involved, I'm assuming you are the legal father.
If they continue to give you trouble, give me a call and we can see what we can do. Good luck.
This should not be considered legal advice, but rather simple information. You should consult a lawyer to review your unique situation. No client-lawyer relationship exists until you sign something indicating there is.