jealous boyfriend

Hey ladies. 
I've been dating this guy for a year now, he's sweet he loves me very much he is great with my child. BUT he's super jealous and hates that I'm friends with my child's father which he new from day one that we have a good relationship we were always more friends and it's great for our child. In the beggining he was fine with it but now he's not ok with it and makes it very obvious. A few examples 
One night we were going out with a group of friends, I put on a skirt and he said no wear jeans at first I thought he was thinking of the cold weather but then it felt more of a controlling thing. 
This one night my child's father was over hanging out with our daughter, he asked me if he could come over and I said not tonight I was tired and already in bed while my daughters dad was getting her to bed, he asked me if my ex was there it was very random I said yes he is, he lost his shit and said he'll be over and he better not be there when he gets here, I kept saying please respect that I just want to go to sleep I'll see you tomorrow anyway I fell asleep! Well my daughters dad ended up falling asleep in my child's bed, in the morning I woke up to 40 missed calls 80 plus messages and photos of my exes car, he had walked over at 12am- I totally get that how he would have felt seeing his car and what he would have been thinking, I didn't hear the end of it I felt very creeped out like he owned me. It frustrates me because I know that I wouldn't go there with my ex and I wish he would trust me. 
Whenever he sees that I'm online he'll message me asking who I'm talking to and then he'll ask if I'm still talking to them. 
On the weekend my ex brought over some furniture for my mum, again I got introuble for that because when my ex got
To mine I said I'll take you home now he was going home anyway and I was saving the awkwardness for him because I know he's shy and uncomfortable with it. so I get yelled at that I'm choosing me ex over him and that I want to spend time with him, he can't even register that he would want to spend time with his daughter and that it's not about me and my ex it's about our child. 
There is so many stories I could tell, like looking at another guy is a no go. He goes through my phone every chance I get. Deletes guys off my social media that I don't even talk to- hell he deleted a guy I was talking to about gardening!
I give him no reason for this jealousy and if I wanted to be with my ex trust me I would be with him! 
I'm more shocked at myself because I am a very strong person and I don't take shit or possessive behaviour, this isn't like me to not be clear headed on a situation. I guess I'm hoping this jealousy will go away or he will grow out of it? Or am I in the wrong for being close friends with my ex? Even though I made it very clear from day one because my child's father is important to me and it makes me happy seeing my daughter see her parents getting along. I came from a shit split parent house hold with yelling and mean step parents and that's the last thing I want my child to go through! I've tired to get him to meet my ex but he won't have a bar of it. 
Has anyone been in a similar situation? Does the jealousy stop? Thanks girls.