Hi @JoJo2106. I have no doubt that it is distressing to see what he is saying on social media. But I am afraid there is little that you can or should do about it.
When my ex wife and I separated, she spent a lot of time running around the small town where we live spreading all sorts of lies about me. It was a defence mechanism. The truth is that we split because of her violence towards me, and a long pattern of aggressive, controlling, and jealous behaviour. She had some challenging mental health problems. When we split, all that fake narrative that she'd created in her head got spread around town. None of it was true, but there were some people who believed her. And I lost a few friends.
But throughout it all, I held my tongue. The only people who suffer when parents start publicly trashing each other are the kids. So I kept quiet. Only a few trusted friends were told the truth (because we all need someone to talk to). As for the rest, if someone explicitly raised one of the rumours with me, I would tell them it wasn't true.
I relied upon people who truly know me seeing through the lies for what they were. And the majority of people did exactly that. As for the rest - I figure those people probably weren't a great loss.
I found that the best thing I could do was focus on providing my daughters with the consistent, stable presence that they needed; and on being the best dad I knew how to be. And that's what I've done for the past two and a half years. And all those people she was talking to heard what she was saying, and they also saw the reality. They saw me day in and day out being a great Dad (I know it's not modest - but I AM a great Dad 😁) and a decent human being. They saw me stay single, while I concentrated on my girls and on my own healing from the abuse. And they saw her behaviour - the rages, the rush to move a new bloke in with her as soon as she moved out of the FMH. And they drew their own conclusions.
Block your ex on social media. If people start telling you what he's doing on there, politely tell them you don't need to know. From this point, the only interest you need to take in him is in ensuring that your kids are okay. Be your best you, and live your best life. Focus on what matters. The rest has a way of sorting itself out.
Two and a half years down the line, my life is amazing. The girls and I are happy. Nobody cares about the nonsense my ex was spouting back then. It gets better. Good luck.