Secondary sources refer to our subject as James M. WYATT, but I've yet to find a primary record giving him a middle initial.

.  William Harrison WYATT, b. 6 Dec 1816?; d. 1837, Calloway Co., KY
.  Mary Frances WYATT, b. 1818; m. H.J. SMITH
.  John T. WYATT, b. 1820

The fact that the AF is wrong about these three make me wonder if Hannah, Nancy, and Judah are correctly attached to these parents.  That is, they had daughters those ages, but were they those daughters?  I am assuming Rachel is correctly ascribed to James, from which Gracie, William (b. 1835), and Thomas follow. 

The AF shows a William Harrison WYATT as eldest son of James M. WYATT.  It has W.H. born in North Carolina, married to Susan Caroline BAZZELL, and deceased in 1837.  But as shown by William & Susan's 1850 Census record, William was born in Kentucky, not North Carolina, and obviously, he did not die in 1837.  William Harrison WYATT, husband of Susan Caroline BAZZELLl, is actually the son of McGilvery & Lucretia (DUNN) WYATT. 

1.  Marriage Record:

2.  1820 Census Index and Digital Images (online at Ancestry.com; Image #26 of 45; extracted by Diana Gale Matthiesen):

1820

NC

Mecklenburg Co.

p. 187

Ln. 10

James Wyett

000100-00100-0-100

no slaves

Sylvester's data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	19-25*	1794-1801	= James (b. 1797)
1 female	16-25	1794-1804	= Wife
1	person engaged in agriculture
*In the 1820 Census, the third column is age class 16-18 and the fourth column is age class 16-25; therefore, any individual in column three is duplicated in column four.  By subtracting the number in column three from the number in column four, you can create an age class "19-25."

Listed one line below James's father, Sylvester WYATT, and two lines above James's brother, John WYATT, who is six lines above their brother, David WYATT.

3.  1830 Census Index and Digital Images (online at Ancestry.com; Image #51 of 176; extracted by Diana Gale Matthiesen):

1830

NC

Mecklenberg Co.

p. 26/330

Ln. 12

James Wiett

000 001 - 220 001

210 000 - 001 000

These data indicate:

No., Race, Gender	Age Class	Therefore Born	Individuals Inferred
1 white male	30-39	1790-1800	= James (b. 1797)
2 white females	4 or under	1825-1830	= Judah (b. 1828) = Nancy (b. 1826)
2 white females	5-9	1820-1825	= Rachel (b. 1823) = Hannah (b. 1822)
1 white female	30-39	1790-1800	= Wife
2 male slaves	9 or under	1820-1830	= ? ?
1 male slave	10-23	1806-1820	= ?
1 female slave	24-35	1794-1806	= ?

Listed next to Thomas WYATT.  On the next page is James's father, Sylvester WYATT, and on the next page is James's brother, John WYATT.

4.  1840 Census Index and Digital Images (online at Ancestry.com; Image #43-44 of 106; extracted by Diana Gale Matthiesen):

1840

KY

Calloway [now Marshall] Co.

pp. 74B-75A

Ln. 1

James Wiatt

200 000 100 - 000 000 000

200 000 - 000 100

0300000

These data indicate:es

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 white males	4 or under	1835-1840	= Thomas (b. 1838/9) = William (b. 1835)
1 white male	40-49	1790-1800	= James (b. 1797)
2 male slaves	9 or under	1830-1840	= ? ?
1 female slave	36-54	1785-1804	= ?
3	persons employed in agriculture

James's wife is recently deceased.  The daughters must all be living with other kin.  Listed 19 lines from James's father, Sylvester WYATT.

5.  1850 Census Index/Microfilm (online at GenealogyLibrary.com):  Marshall Co., KY, p. 447, 231/231, enumerated 9 Aug 1850 (extracted by Diana Gale Matthiesen):

Martin Lyles	26	M	Farmer		Ky
Rachel   "	26	F			NC
[Martin and Rachel's children]
William Wiett	15	M	Farmer		"
Thomas    "	11	M			"
Gracy     "	17	F			"

6.  LDS.  Family Search: Internet Genealogy Service: IGI - International Genealogical Index and AF - Ancestral File (online at FamilySearch.org).