can my ex husband send my childs dentist a letter with his name, ESQ on it saying he is not responsible for any payments, een if he is order to pay ha

Several different questions. Technically, "Esq." when used in America means "lawyer," so if your ex is in fact a lawyer, it is a proper title, like "Dr."  If he is not a lawyer, it not legitimate to do so, although it is hard to imagine anyone prosecuting such a misrepresentation unless he was using it to defraud someone out of money, etc. As to whether he is or is not responsible for dental bills, it depends on the underlying court order, and facts.  Normally, medically necessary medical procedures are split between the parents.  Consult your written order, and then consider seeing a family law specialist.  Meantime, some background is posted at http://willicklawgroup.com/child-support/.