Back story:

So me and my SO got together June 21st and have been together ever since no cheating no nothing it was great well I'm 28 weeks pregnant that came to a shock to everyone because he had told me he couldn't have kids so we never used protection and now we are having a beautiful baby boy and everything was going so good well we have a mutual friend who I did in the past have a thing with nothing serious on my end but on his I feel like he was in love with me so I cut it off a long time ago before I even knew my SO well this mutual friend of ours told my SO that the baby might not be his it might be someone else I hooked up with on june 14th which in my mind didn't even matter because it was before I even met my SO and i got pregnant at the end on July so now everything has just changed we fight all the time he says he dont believe this is his baby I'm literally heart broken over this he wants to get a DNA test and I told him okay we can get one but you would have to pay for it and it will have to be after the baby is born so I told him until he believes the baby is his our son will be given my last name and he did not like that I just dont know what to do anymore like can someone tell me how I can explain this better to this man that this baby is his he just keeps going back to I knew I couldn't have kids every girl I hooked up with never got pregnant but I get with you and you got pregnant so fast like i just dont know what to say anymore any advice would help.