If I am right, your Paul is Carnelias (Cornelius?)(one of 2 census spellings) P. (Paul?) Killman born about 1903 in Allen Co. Ky.. He is son of Cornelius or Corneavena (2 of Census spellings) B. Killman b about 1857 and his 2nd wife Elmina, ---all based on circumstantial census records. The Killman family has a long history of living in Allen Co Ky.
Do you have any idea when and where Paul died? A death cert. MAY give Pauls other name. I have been unable to find a social security index listing for him.
If you e-mail you phone number I will contact you about more on that family and ideas for more research.