Thank you so much for all of this information! I am happy to see Emsley as Keziah's daughter in the school record; what a great find! The census records are very confusing, especially in 1850. I can't believe that there are a Lewis and Jesse Siner the exact ages as Lewis and Jesse Mize. I think the Elizabeth listed is probably Keziah, and the boys are her sons. The census taker made so many other errors, and Emsley is listed near them, which would seem unlikely if her mother hadn't already been Jesse's wife. Also Elizabeth would have been much older if she had married Jesse in 1810.It is likely that Jesse and Keziah were married by the time he shows up in Smyth County (I mistakenly wrote Scott County in my first post) in 1840 (his name is spelled Signer).
Lewis Mize did marry Lucinda Estep. They named their first son Randolph, which is what drew my attention to them. Emsley is "Shiplet" in 1860 with three sons, including two born after 1850. Whether she was married or widowed at the time is an open question. I don't know who that first husband was, but if her son William was born in Sullivan County in 1847, there may be some clues there.
On the 1870 census (I think) Keziah said she was born in Wake County (NC). She and Emsley both gave a variety of ages for themselves, but if she were the daughter of Randolph and Martha, she would have been born around 1805, because they were in Rowan/Davidson by 1808. And Emsley was probably born in 1827 rather than 1829, which would match the school record.