A little squirt of cold water!
You may want to squirt some cold water on him the next time he comes around to your door. It won't hurt him but it might discourage his closeness to your cats and door. If he is a stray, he could be ill and you certainly don't want your kitties to tangle with him through a screened door or window. They can still get claws to each other through the screens. Have you thought about having animal control trap him and take him away? It may end his life, and yet if he is sick, you don't want him to be spreading any disease that is contageous. I don't want to frighten you though. He could be the neighbor's cat!
Keep us posted!:eek: