My ex has done/is doing this same thing to me. He was emotionally and physically abusive throughout our marriage. He controlled every aspect of my life, from who I saw, where I went, right down to what I wore and what music I listened to.
He was very good at the subtle abuse. He'd be the most amazing partner/father in front of people but behind closed doors was a different matter.
I reached the end of my tether when our twins were 3 months old. I was suffering from PND and he told me it was my own fault as I didn't go out and didn't have any friends (who's fault was that?) So I made more effort to get back in touch with old friends and arranged a night out. I got home and he beat me for going out.
I asked him to leave and he did. But told everyone he had left me as I was a serial cheat.
He posted all manner of accusations on Facebook. I lost a lot of so-called friends over his lies. It upset me massively.
He told people I was on medication as I'm 'mental'. He told people I'd had an emotional breakdown because I missed him so much. He called social services and told them I self harm in front of the children, that I'm a cocaine user and take it while the children are in the house, that I'm an alcoholic and I regularly drink drive with the children in the car. He even went as far as to say he would only sign the divorce papers if I stated in them that I had cheated!
It's taken me a long time to realise that what he's been saying and doing was just another way to try to control my life when he realiased he had no hold over me any more. I also no longer give a flying fuck care what the people who believe him think of me.
I have a very close set of friends and a very supportive family who know the whole story. If people want to believe his ridiculous stories and accusations then they're not people I want in my life and their opinion matters not one iota.
I have been tempted in moments of anger to get in touch with these 'friends' I lost and explain what's actually gone on. But I pulled myself round and decided that my dignity was worth more than the waste of time that would actually be.
It takes time OP and it is very very hard. If you're in a position where you can go NC with him I would absolutely suggest you do that. I don't have that luxury unfortunately.
I recommend a book called 'Why Does He Do That' which will help you to understand why he does and says these things.
Good luck.