Child with a previous relationship

I'm having a really hard time in my relationship right now. My oldest child is from a previous relationship. My child's father and I are currently co parenting but it's difficult for me because of the relationship I'm in now. I've been with this man for 5 years and he always have a problem with everything I do with my child's father which is barely nothing at all. My boyfriend says me and my childs father should only converse about the child nothing more. I respect. So about to weeks ago my child's father message me about dropping my child off. We began messaging back and forth but I promise it was only about the child. When I looked at the time it 1am. When I realize how late it was I told him it was a lil inappropriate for us to be texting this late that I'll call him tomorrow. He then apologized and that was it. Every conversation we've been having is about my child. All the messages everything is there. Now current boyfriend is pissed because he saw the messages. He treats me like shit when hes upset. And I'm hurt because he always gets mad for bullshit and treat me like im doing him wrong. Its stressful because im a loyal woman and it not fair to be treated like im cheating when im not. I love him so much so the fact that hes giving the cold shoulder and not tlking to me hurt me but fuck that I didnt do anything wrong what's so inappropriate about this convo