How do I stop letting this bother me?😣🤦🏼‍♀️

I broke up with my sons father when I was pregnant because he was being verbally abusive and manipulative. I let him know that he is more than welcome to be involved with his son, but I was no longer interested in a relationship with him. He only came to visit him 2 times before moving to a different state. The 2 times he did come and visit he only stayed for 45 minutes and left. When I asked him to be more involved he said he can’t because he hates me? Anyways, the reason I am bothered is that he keeps posting photos of the baby on social media and saying that our son means the world to him and is pretending to be this super involved dad when in all reality, he hasn’t seen his baby in months and lives in a different state. The photos he’s posting aren’t even recent. All of the comments are his friends and family praising him for being this amazing dad when in all reality he doesn’t pay any child support, see his child, or even bother to text and ask how he’s doing. I am doing this all by myself. I know this sounds stupid but it really bothers me. Anyone else gone through this and have any tips?