Telling him

Okay, so a ex of mine is telling people that he is the father of my son. My son is 10 months old and I haven’t talked to my ex since April or May. My ex is definitely not the father, I even told him this. My boyfriend is the father. I really want to tell him what is being said. My boyfriend doesn’t live with me or even in my town. So he doesn’t know. However, everyone is telling me not to tell my boyfriend. But I feel like that’s betrayal or something... what should I do?