My primary research is the Frailey line of Daniel and Elizabeth Frailey but there were so many Ledbetters in my file that I wanted to connect them. I checked and I have no direct relationship with this family. You have more info on Narcissa's descendents than I do but I have anestors back to her GGGrandfather if you don't have this info and want it.
I will contact my ledbetter source and see if he has more info on Narcissa for you. If you want the ancestors of Narcissa let me know here and I will send it to you by email.
I will try to find out where Round Hill cemetery is for you also.

Here are the census records I have for John Marshall Ledbetter

1850 IL Hardin Township A Im 36 page 42
Sept 2nd
305-305 William Hobbs 25 M farmer born TN
Amanda Hobbs 25 F born TN
Ann Hobbs 4 F born IL
Susan Hobbs 2 F born IL
Minerva (????) 22 F born IL
Marsh Ledbetter 20 M born IL

Marshall is also listed with mother an stepfather in 1850 census.

1850 IL Hardin Township A Im 61 page 67
Sept. 11th
475-475 James Mott 26 M farmer born KY
Arnna Mott 37 F born TN
1850 IL Hardin Township A Im 62 page 68
Daniel Ledbetter 17 M farmer born IL
Charity Ann Ledbetter 16 F born IL
Susan Mott 11 F born IL
Sarah Mott 8 F born IL
Sophia Mott 6 F born IL
James Mott 4 M born IL
Betsy Mott 2 F born IL
Vida Mott 1 F born IL
John Mott 1 M born IL
Martha Mott 7/12 F born IL
Marshall Ledbetter 20 M farmer born IL

1860 IL Hardin pg 44 Township 11 Range 8 Im 27
268-268 Marshal Ledbetter 29 M daylabor born IL
Rebecca 20 F born IL
Caroline 2 F born IL

No Narcissa here in 1860 and no Caroline in 1870
I had always thought Narcissa died but you have other
info so her name may be Carloine Narcissa or Narcissa Caroline.

1870 IL Hardin Rock Creek pg 13
92-92 Ledbetter Marshal 40 M farmer IL
Rebecca 36 F kpghouse IL
Narcissa 13 F @home IL
James 10 M @home IL
Martha 3 M @home IL
Charity 1 M @home IL

1880 IL Hardin Elizabethtown pg 422B

Name Rel Mar Sex Age BP Occ FBP MBP
John N. Ledbetter Self M M 50 KY Real Estate KY KY
Rebecca O. Wife M F 40 IN KpgHouse KY OH
Mollie V. A. Dau S F 19 IL At Home KY IN
Mattie Dau S F 15 IL At Home KY IN
John N. Son S M 8 IL KY IN

Source Information:
Census Place Elizabethtown, Hardin, Illinois
Family History Library Film 1254211
NA Film Number T9-0211
Page Number 422B

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Hope this helps Jackie