They are so good at manipulating and twisting things. What helps me is I remember that to them feelings are facts. They will twist what we see as facts to fit their feelings and in doing so come up with completely different "facts". It is like me and my ex are speaking two different languages and there is no common ground. eg you can't reason with a Aussie by speaking Chinese to him, it ain't gunna work.
People your ex speaks to are getting his version and in it you are painted black, that is his reality. (Not the reality that the rest of humanity lives in but that's beside the point
) You cannot fight that. For me I have learnt to shrug and accept some people believe him and those that matter to me know what he says is not the whole truth. It's hard and at times has been unbelievably frustrating but I've had to learn to let go or else I would just keep butting my head against a brick wall and get a headache and achieve absolutely nothing.