Need advice please.

Hi Ladies.

So I'm with my bf for 4 years now and in the second year of our relationship I cheated on him with on of my ex bf but it was once off and never happened again but every time we bump into the ex we have arguments that never end. My question is how do I show my bf that he's the one for me and that I'm sorry? Because he still have some type of fear that it might happen again and from my side I'm forever sorry that I did what I did but my bf just can't see past that mistake