I think WIlliam H. could be the Henry, son of James Rogers I found in 1900. In 1910 William H. is living right in between Henry Little and James Rogers. This was the only Clemmie Rogers/Rodgers in Martin County.

1910 Census Beargrass, Martin Co., NC
William H Rogers Head M B 30 married 9 yrs 1st marriage b. NC Father NC Mother NC Occu: Farmer
Mary Rogers Wife F B 30 married 9 yrs 1st marriage 5 children born 3 living b. NC Father NC Mother NC
Clemie Rogers Daughter F B 8 single b. NC Father NC Mother NC
Lon (Don?) M. Rogers Son M B 3 single b. NC Father NC Mother NC
Arthur R Rogers Son M B ?mons Single b. NC Father NC Mother NC

next-door

James Rogers Head M B 59 married 24 yrs 2nd marriage b. NC Father NC Mother NC Occu: Farmer
Cora Rogers Wife F B 43 married 24 yrs 1st marriage 8 children born 7 living b. NC Father NC Mother NC
Annie Rogers Daughter F B 18 single b. NC Father NC Mother NC
Chulsie Rogers Daughter F B 15 single b. NC Father NC Mother NC
Olliller? Rogers Daughter F B 10 single b. NC Father NC Mother NC
Harrett Rogers Daughter F B 3 single b. NC Father NC Mother NC
Theodore Rogers Son M B 2 single b. NC Father NC Mother NC

1920 Census Bear Grass, Martin Co., NC
William H. Rogers Head M B 41 married b. NC Father NC Mother NC Occu: Farmer
Mary J Rogers Wife F B 40 married b. NC Father NC Mother NC
Clemmie J Rogers Daughter F B 16 single b. NC Father NC Mother NC
Loy? Macky Rogers Son M B 12 single b. NC Father NC Mother NC
Arthur Ray Rogers Son M B 10 single b. NC Father NC Mother NC
Levi W Rogers Son M B 8 single b. NC Father NC Mother NC
Robert Rogers Son M B 6 single b. NC Father NC Mother NC
William A Rogers Son M B 4 single b. NC Father NC Mother NC
John H Rogers Son M B 2 single b. NC Father NC Mother NC

Finally found the Rogers in 1870!!! Their name was misspelled Rogero in the index. It was spelled Rogers in the original document, however.

I know the 1880 Census claimed she was 14, but based on later census data, that could be an error. If she was born in 1872, it would make sense that she isn't recorded here.

1870 Census Williamston, Martin Co., NC
Rhoden Rogers 50 M B Farm Hand b. NC
Jennie Rogers 23 F B Farm Hand b. NC
Harriett Rogers 20 F B Farm Hand b. NC
James Rogers 20 M B Farm Hand b. NC
Mary Rogers 19 F B Farm Hand b. NC
Pender Rogers 18 F B Farm Hand b. NC
Celia Rogers 18 F B Farm Hand b. NC
Drucilla Rogers 13 F B Frm Hand b. NC
Sam Rogers 3 M B b. NC
Malvina Rogers 2 F B b. NC
Henry Rogers 1 M B b. NC

Rhoden appears to have died before 1880.