Matthew is supposed to be the third son, but his birthyear makes that unlikely, unless Mary Ellen and William were twins.

1a.  Jordan R. Dodd, ed.  1993.  Kentucky Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-229):

Clark, James	Stubblefield, Susan S.	29 Jan 1817	Christian Co.
Cabaniss, Ethan T.	Clark, Mary Ellen	21 Jun 1844	Christian Co.

1b.  Marriage Index:  Kentucky, 1851-1900.  Liahona Research, Orem, UT (Broderbund CD-233):

Gary, John C.	Clark, Eliza S.	9 Dec 1851	Christian Co.
Fox, Dr. Newton	Clark, Lucy Ann	21 Jul 1852	Christian Co.
Gary, Robert S.	Clark, Martha Lacy	3 Nov 1857	Christian Co.
Shanklin, Charles O.	Clark, Sue J.	21 Oct 1868	Christian Co.

1c.  Anon.  1983/96.  Kentucky Marriage Records: from the Register of the Kentucky Historical Society.  Genealogical Publ. Co., Baltimore, MD (Broderbund CD-519):

p. 101

Clark, James........29 Jan., 1817 Stubblefield, Susan d. of Ben T. Stubblefield    John Gaines

This publication is rife with errors, and the given name of Susan's father is one of them (someone apparently read "Bev." as "Ben.").

2.  1850 Census Index/Microfilm (online at GenealogyLibrary.com):  District No. 2, Christian Co., KY, p. 379B, 295/318, enumerated 2 Sep 1850 (extracted by Diana Gale Matthiesen):

295	318	James Clark	58	M	Farmer	5430	Virginia
		Susan S  "	52	F			"
		Lucy A   "	25	F			Kentucky
		Eliza S  "	23	F			"
		Emma V    "	21	F			"
		John W     "	21	M	Farmer		"
		Francis M   "	16	F			"
		Alexander C "	15	M	Student		"
		Richd S     "	13	M			"
		Martha L    "	11	F			"
		Susan J     "	9	F			"
		James M     "	27	M	Farmer		"
	319	Mary E Cabanis	32	F			"
		Susan J   "	1	F		1224	Illinois

Why is James listed last?  Usually that means he is either the son of a prior marriage or not a son, at all.  Daughter Susan is living with James in 1860 (see next source).

3a.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #

3b.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #178 of 267):  Hopkinsville P.O., Christian Co., KY, Roll M653_362, p. 707, PN 59, 402/402, enumerated 13 Jul 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

James M Clark	34	M		Farmer		7000	Ky
Elizabeth L Clark	25	F					Ky
Charles L Clark	8/12	M					Ky
Susan J Clark	18	F				3000	Ky

4.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #2 of 60):  Hopkinsville P.O., 4th Civil District, Christian Co., KY, Roll M593_455, p. 442B, PN 2, 10/10, enumerated 16 Jul 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Clark James M	45	M	W	Farmer	18600	1500	Ky
_____ Ben C	8	M	W				"
_____ James	78	M	W	Work on farm			Va
Dickenson Phebe?	25	F	B	Domestic Servt			Ky
_________ Eliza	10	F	B	"      "			"

5.  J.H. Battle, ed.  1884.  County of Todd, Kentucky:  Historical and Biographical.  F.A. Battey Publ., Chicago (online at the Kentucky Biographies Project).
On p. 322, under the heading "Trenton Precinct":

MRS. LUCY A. FOX was born in Christian County, Ky., April 11, 1824, and removed to Todd County in 1838, where she still retains her residence.  She is the honored daughter of James Clark, who was born in 1791, reared at Frankfort, Ky., and served his country as a gallant soldier in the war of 1812, and died in 1877.  He was the son of Matthew Clark, a native of Virginia, who died in Kentucky about 1830.  Subject's mother, Susan S., daughter of Col. Beverly Stubblefield (of Revolutionary fame) and his wife Mary (Shelton), was born in Virginia, 1797, and died in Kentucky in 1854.  Their children are:  Mary E. (Cabaniss), Susan J., Matthew B., James M., Lucy A., Eliza S. (Gray), Emma V., William, Joseph A., Frances M. (Garnett), Alexander C., Richard S., Martha L. (Gary) and Susan J. (Shanklin).  Subject was married July 19, 1852, to Dr. Newton Fox, of Todd County, Ky.  He was a native of Danville, in this State, and died in Todd County in 1855, at the age of fifty-two years.  As a result of this union two daughters were born, viz.:  Susan S. (Byars) and Lucy N. (Byars).  Mrs. Fox is the owner of 150 acres of very productive land.  She is a Baptist and is remarkable for her extensive knowledge of standard works and current literature.

6.  William Henry Perrin, ed.  1884. County of Christian, Kentucky: Historical and Biographical.  F.A. Battey Publ., Chicago.

7.  J.H. Battle, W.H. Perrin, & G.C. Kniffin, eds.  1887. Kentucky, a History of the State.  F.A. Battey & Co., Louisville, KY (excerpts online at the Kentucky Biographies Project):

M. B. CLARK, Muhlenburgh County, was born December 4, 1819, in Christian County, Ky., and is the third of fourteen children, six boys and eight girls (thirteen lived to be grown) born to James and Susan S. (Stubblefield) Clark, natives of Virginia; the father was a son of Matthew Clark, who married Mary Shelton, a native of Virginia; he moved to Franklin County, Ky., in 1811, where he purchased and improved a farm; was a soldier of the Revolution, and was quartermaster in Shelby's brigade in the war of 1812.  James Clark was a captain in the war of 1812, his wife was a daughter of Beverly and Mary (Shelton) Stubblefield; Beverly Stubblefield was a colonel in the Revolution, and came to Kentucky in 1812, and settled in Todd County near Trenton, where he purchased and improved a farm of 1,300 acres...

Were both of Matthew's grandmothers named Mary SHELTON?