I'm really sorry you've been going through all this.
I doubt he has mental health issues. Or rather, if he does they aren't what are causing him to behave like this. He's continuing to gaslight you because it's a means of trying to control you, which is all the abuse is about.
All you can do is try to limit his reach and impact. Don't engage. Just remind yourself "he is gaslighting me again, I know the truth, and it isn't what he's saying". Just repeat to yourself whatever variation of "I know the truth about what happened" helps you.
I assume your only communication with this man is in relation to him seeing your child?
If you haven't already, create a separate email address only for communication in relation to your child. Block him from your other address. Or, create a new one he doesn't have.
Then only check it once or twice a week at a set time. Make it clear when emailing him that if you require a response and he doesn't reply by x date, then it will be too late. Stick to it, regardless of the games he plays or accusations he throws at you (remind yourself you know his tricks, and you're not being sucked into it anymore).
Likewise, if you can have a separate SIM card in a cheap phone for that purpose. I assume he has your child to stay with him? If so, you can use that phone number for emergencies. Then you only have to check it during those times.
If he writes anything that isn't about your child that needs action, then ignore it. Do not respond, do not correct him, do not debate. Just act like he hasn't said anything.
If he sends you messages that do not even say anything relevant to your child, then delete them. You don't have to read his words. They're meaningless.
You may not be able to stop him trying to mess with you by email/in writing, but you are in control of what you do with his messages, how you respond to them, and you have the power to relegate him to a second email address that is only checked once a week.
Focus on the ways you can take some control. Feeling less powerless will hopefully help make it easier.
Remember, he's doing this because he's lost and has no other reach to you anymore. The fact he's doing this is a reflection of how strong you are and how well you're doing, and the fact that you've taken the power away from him. He can't stand that he has no control over you, that's why he keeps doing this. But he's never getting it back.
You know the truth of what happened to you. As do the police and other agencies who got involved. His silly games don't change that.
Take care of yourself tonight. Is there anything nice you can do for yourself? A favourite film or book?