Hello! Please remember that my responses are informational only, we are not establishing a therapeutic relationship.
I think trying to look at what might be underneath his jealously could be helpful. Most likely he can't verbalize what it is --he's expressing all that he knows how to express. Here's some possibilities:
1. Maybe he is scared of losing you (Even if his father is involved, it's not in an intact family. Even if he has no memory of you and his father being together --there still can be a sense of loss).
2. Maybe he is expressing the desire for more attention from you - (Please note this can happen even if you are giving him TONS of attention. It never seems like it's enough for many, many kids at this age).
Solution? Let him have his feelings. You can tell him what you want --like if you are going out you might say, "I am going out on Friday night. We will go to the park together on Saturday."
You can empathize and validate his feelings (this doesn't mean you agree that you shouldn't have a boyfriend). "I know you get upset when I have a boyfriend and you'd rather I didn't. Please know that I love you the same no matter what. I always will."
Letting him have his feelings doesn't mean that you don't put boundaries on his behavior (i.e. no hitting, screaming, saying mean things, throwing things, etc) --but he can cry, hit a pillow/punching bag, say he doesn't like it.
It's no fun to let the little ones have their intense emotions, but it's emotionally healthy for them to be allowed to have them, to be validated for them, and to be taught what is an appropriate (vs. inappropriate) way to express them.
I hope that helps ---