Birth records are not commonly found for births in 1816 as most births were recorded by a family member in a family Bible. Birth certificates were not common in the District until 1874. You might be able to find a christening record, but you would need to know which denomination the family was a member of.

It appears your William Wise was born in the District of Columbia. but later resided in Kansas. Have you checked any of the Biographical Histories to see if any of his sons or daughters are included. Most biographical entries include some historical information about parents and sometimes grandparents. The Kansas Historical Society might be a source for such information.