The annual report of deaths to the Kentucky state auditor for Morgan Co. lists John Caskey, age 85, married, born Bath Co., died 22 Jan 1878 in Morgan Co., cause of death old age, parents Thomas & Lydia Caskey, father born NY, mother born NJ.

1850 census of Morgan Co., Ky, lists as family #282:
John Caskey, Sr, 56, NY; Hannah, 52, NY; Miles, 24, Ky; Mary, 21, Ky; Elizabeth, 19, Ky; Robert, 17, Ky; Mary, 13, Ky.

1860 census of Morgan Co., Ky, district 1, enumerated 4 June, lists on p. 1 as family #2:
John Casky, 66, farmer, b. New York; Hannah, 63; Mary, 26; Robert F., 24, farmer; John Amyx, 21.

There are dittos in the birthplace column for all household members after John, but Hannah and the others were definitely not born in New York, and John probably wasn’t either.

The next household is headed by Peter Amyx, who is married to their daughter Diadamia. They are the parents of the John Amyx in this household.