An inheritance would not be "Shared" with your ex; however, the inheritance is income for child support purposes in the year it is received. If your ex learns of the inheritance, he/she can petition for an increase in child support.
This depends on several factors: the contents of the divorce decree (if there is one); the contents of your father's will (if there is one); and the contents of the child support order. I would suggest having an attorney review these documnents for you to provide a more thorough response. I can recommend a firm in your area if you would like.
The inheritance is your separate property and you will not have to divide it with your ex. However, the inheritance and/or the annual income generated by the inheritance may be considered additional income by a court for purposes of calculating child support.