Have you located proof that a child was born in 1813 to a couple married in 1776?
Supposing the bride was 16 at marriage, she would have been 53 in 1813.

Robert BARNES' MD Marriages, St. Mary's Co., MD, by Reverend James WALTON, S. J. (Catholic),
FENWICK: John, 11 Nov. 1772, Mary THOMPSON
Thomas, 3 July 1774, Eliz. THOMAS
Philip, 3 Sep. 1779, Rebecca GREENWELL
Jacob, 12 Je. 1776, Henrietta HOWARD.
[Jacob could be translated James, but Henrietta probably wasn't Hanna.]

MD Deponents: Cuthbert FENWICK, aged 40 in 1654. Ignatius FENWICK, 28 in 1769, moved to St. Anthony's in PG Co. in 1763.

Among the earliest in MD Calendar of Wills are those of Cuthbert & second wife Jane FENWICK. Cuthbert's was made 6 Mar. 1654, date of proof not listed, & named sons Cuthbert, Ignatius, Robert, Richard, and John. Widow Jane CUTHBERT, of Patuxent, Calvert County, will pr. 1660, named stepsons Cuthbert & Ignatius, and sons Robert, Richard, & John. No stock was to be sold until Cuthbert was 21, and guardians of younger children were to be Cuthbert & Ignatius at 21.
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MD Cal/o Wills:

Richard FENWICK, SM, 1 & 26 Apr. 1714. To sons Richard, Cuthbert, John, & minor sons Enoch & Ignatius. Sons by first & second wives to share equally. Should disagreement arise, bro. John to make division. Wit. Jos. ALVEY, Geo. PLOWDEN, Cuthbert SAWELL.

Ellen FENWICK, St. Mary's Co., 7 Aug., 1 Nov. 1737. To ch. Ellen, Philip, John, Ignatius (ex.), George, & Richard. Will mentions personalty from her sons' father's estate. Wit. Geo. CLARKE, Matt. & Jas. BURNE.
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Since the first Cuthbert of MD had five sons in southern Maryland, all minors in 1660, so apparently born after 1640, there were lots of FENWICK families by the 1770's. I looked in MD Calendar of Wills, but I couldn't find proof of a direct line for a James. This may be father of James, from MD Cal/o Wills:

Ignatius FENWICK, St. Mary's Co., 24 Jan. 1776, 8 Oct. 1776. To son Edward, "St. Marys Hill" & pt/o "St. Peters" if he pay son Henry a hundred pounds sterling at 21. To son James, "Holdons Hole," if he pay to sons Joseph & Henry at age 21. To son Richard, pt/o "Drapers Neck." To son John. To son Joseph, pt/o "Poiney Point." To son Henry, "Millmans Adventure," & pt/o "Small Hope." To daus. Elizabeth FENWICK, Ann CLARK, Mary J[E]NKINS, to include each daughter's share of estate left by her grandfather COLE. Wit: Richard McKAY, Kennady & Wm. HEBB.

Will of Edward COLE, St. Mary's Co., 26 Mar. 1761, 21 Dec. 1762. To wf. Ann. To dau. Mary FENWICK, grandson Ignatius FENWICK, and Mary FENWICK'S children living at the time of my death...
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Abstracts of Inventories of the Prerogative Court of MD:

Cuthbert FENWICK, 4.515, CA, #13103 & 15459, 27 Oct. 1677. Administrator Richard FENWICK.

Mr. Cuthbert FENWICK, 15.603, SM, 20 May, 11 July 1730. Next of kin John & Cuthbert FENWICK. Admx. Mrs. Elisabeth FENWICK.

Mr. Ignatius FENWICK, 17.23, SM, 6 D. 1732, 8 Mar. 1732/3. Appraisers Wm. CANADAY, Thos. HEBB. Next of kin [NOK] John & Enoch FENWICK. Admx/exx. Ellenor FENWICK.

Mr. John FENWICK, 18.315, SM, 15 Mar. 1733, 4 Je. 1734. NOK: Edmund PLOWDEN, Cuthbert FENWICK. Admx/exx. Winefred FENWICK.

Cuthbert FENWICK, Jr., 33.45, SM, 29 Jan. 1745, 4 Je. 1746. NOK Robert FENWICK. Admr/ex. Benjamin FENWICK.

Richard FENWICK, 36C.55, SM, 21 May 1715. Legatee Elisabeth ALVEY. Coexecutors Richard, Cutburt {sic}, John, Enoch, & Ignatius FENWICK. [Note that Ignatius was a minor in 1714 but a coex. in 1715, so prob. b. ca. 1696.]

Philip FENWICK, 42.215, SM, 5 Apr., 1 May 1750. NOK, Ignatius & Richard FENWICK. Admx/exx. Mary FENWICK.

Joseph FENWICK, 66.220, SM, 26 Mar. 1759. NOK Elisabeth SPALDING, Benj. FENWICK. Admr/ex. Robert FENWICK.

Enoch FENWICK, 66.234, SM, 2 Feb., 8 Mar. 1759. NOK Joseph FENWICK, Wm. JOSEPHS. Admr/ex. Ignatius FENWICK.

Mary FENWOCK {sic}, 67.324, SM, 14 May, 20 Aug. 1759. Next of kin Benedict & George FENWICK. Admx/exx. Eleanor FENWICK.

Richard FINWICK {sic} 65.239, SM, 3 Apr., 2 May 1758. NOK Geo. & Ignatius FENWICK. Admx/exx. Ann FENWICK.

Cuthbert FENWICK, 80.167, SM, 8 Sep. 1762, 4 Mar. 1763. NOK Geo. FENWICK, Athanathus FORD, Jas. BUTE. Ex. Bennett FENWICK.

Richard FENWICK, 86.60, SM, 8 Je., 2 Oct. 1764. NOK Ignatius & Benjamin FENWICK. Admr. Geo. FENWICK.

Benedict FENWICK, 102.183, SM, 25 Apr., 10 Nov. 1769. NOK Ignatius FENWICK s/o Enoch, Jane FENWICK. Ex. Wm. FENWICK.

George FENWICK, 102.239, SM, 15 July 1769. Mentions cousin Enoch FENWICK. Admx. Belinda FENWICK, wid., wf/o Robert FENWICK.

John FORD, Sr., 106.372, SM, 28 Sep. 1770, 5 Mar. 1771. Appraisers Enoch FENWICK, Timothy BOWES. Creditors Philip FENWICK, A. BARNES. NOK Athanathius & Philip FENWICK. Exx. Henitta FENWICK.

Berment {sic, Bennett?} FENWICK, 107.97 & 112.416/8, Apr. 1771, 1 Jan. 1773. NOK Mary Ann & Cuthbert FENWICK. Ex. Richard FENWICK.

George FENWICK, 110.99, SM, 10 Aug. 1772. NOK Benj. & Robt. FENWICK. Admr/ex. James {Jane?} FENWICK. List of debts, 118.228. Exx. Jane FENWICK.

Robert FENWICK, 121.402, SM, 25 Oct. 1774, 28 Jan. 1775. NOK FENWICK, Barbara & Ignatius of E. Admr/ex. Philip FENWICK of Philip.

Elisabeth COLE, 121.418, SM, 16 N 1774, 17 May 1775. NOK Basil HAYDEN, Cuthbert FENWICK. Admr/ex. Chas. HADEN.

Robert FENWICK, 125.255, SM, 10 Je. 1775, 14 July 1776. Next of kin Robert & Bennet FENWICK. Admx. Mary FENWICK.

George FENWICK, 5.220, SM, 18 July 1769. Sureties Enoch FENWICK & Cornelius WILDMAN. Admx. Belinda FENWICK, wf/o Robert FENWICK.

James COLE, 6.174, CH, 17 Je. 1772. Legatees Sarah COLE & Sarah FENWICK. Distr. to James, Mary, Sarah, & Edward FENWICK. Exx. Mrs. Sarah COLE.

Bennet FENWICK, 6.256, SM, 1 Jan. 1773. Sureties Saml. BELLWOOD, Wm. FENWICK. Legatees Cuthbert FENWICK, five daughters. Distr. to ch. Elisabeth, Mary, Richard, Dorothea, Henrietta, Francis, Michel, & Priscilla. Ex. Richard FENWICK.
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Balance Books, estate of:

Robert FORD, 2.9 SM, 30 Jan. 1756. Sureties Enoch FENWICK & Peter FORD. Distribution to widow & grandch. Robert, Margaret, Mary, Joseph, & Ann FENWICK. Ex. John FENWICK.

Richard FENWICK, 2.107 SM, 1 Mar. 1759. Sureties John SPAULDING & Robert FENWICK. Distr. to widow and children: Eleanor, 9 next Nov.; Elisabeth, 7 next Dec.; John, 3 next Apr.; & James, 1 next July. Admx. Ann FENWICK.

Mary FENWICK, 3.26, SM, 5 May 1760. Sureties Robt. FENWICK, John TANEY. Distr. to widow {sic}. Residue to ch. Eleanor (exx. / accountant), Robert, Jennett, Barbara, Philip.

Joseph FENWICK, 4.14 & 4.34, SM, 29 Nov. 1760, 26 Je. 1764. Admr. Robt. FENWICK.

Cuthbert FENWICK, 4.29, SM, 10 Feb. 1764. Ex. Bennett FENWICK.
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I found a family for Ignatius FENWICK on RootsWeb, and I've rearranged the list based on their father's will. There is a lot of misinformation on the family, so I hope you'll post additions and corrections. This is just a work in progress. Land records might provide further clues.

Edward [b. ca. 1740? Named first in father's will]
James [coex. with sister Helena] m. Henrietta HOWARD?
Helena, d. Apr. 1817, Fredk. Co., MD [called FENWICK in father's will]
Ann, m. bef. her father made his will, Ignatius CLARK(E)
Mary, m. ca. 1766, John JENKINS, b. 5 May 1744
Richard
John, d. 20 Aug. 1815, Charles Co., MD; m. 11 Nov. 1772, Mary THOMPSON. [Had John already received an inheritance? He did not receive land per his father's will.]
Elizabeth m. John SMITH [b. 9 Nov. 1754; m. 24 Apr. 1784, per RootsWeb]
Joseph, m. Elenoire MENOIR?
Henry [Two youngest sons were under 21 when father made will.]

Some say there was an Ignatius FENWICK who m. Sarah TANEY in the family of Ignatius who d. 1776, but I don't see him in his father's will. Is it possible that another FENWICK also married a Mary COLE? Edward COLE's will named dau. Mary & grandson Ignatius FENWICK.

GOOD LUCK!