I have found a lot of the same Kissee names you mention, but I've never been able to prove that Thomas Kissee and wife Mahala are Jasper's parents, however I believe them to be.
I found 25 year old Jasper Kissee listed on the 1850 census living with 25 year Thomas and 16 year old Jane. Ozark County Genealogy Society found divorce records where Jane filed after Thomas left the state to return to Kentucky. Then Jasper and Lucinda are listed in 1860 with the family. I'm not sure where Lucinda and Sarah were in 1850. Look for Jasper in the index as Kissal or Kissel. The Kissee/Keesee children are living with John and Sarah Hatfiel in 1870 and in 1880 William and Cynthia Kissee Wrighy are living in Mountain Home Arkansas with their son, Augustus and two of William's brothers and Cyntia's sister Mary. In 1900 I find in Afton, Fulton, Arkansas Sarah Hatfield with William Kissee a boarder. A few houses down is son John Hatfield, wife and son. If you go to the next page, you'll find Sarah's brother, John Kissee and his family, her sisters Cynthia Wright and Mary Wright. Mary was married to William Wright's brother, John Wright.
I would love to find out what happened to Jasper and Lucinda. Why are their younger children living with Sarah in 1870? Did they die of flee the country? I've enen tried to research American southerners that fled to South America after reading that a large group left after refusing to swear allegiance to the Federal goverment following the war and have not been able to find any clues. If you would like to contact me direct you can email me at email@example.com