A part of what I found (much of which is theory) includes:

THOMAS BARKER, m. SARAH _____.
Children:
1. JOHN BARKER b. (Rowley?), MA 9MAR1763, d. Kingsclear Parish, York Co., NB 26SEP1824 age 62 years, m. 20JAN1784 MARY WOODBURY (?) (b. ca. 1764, d. Kingsclear Parish, York Co., NB 30APR1841 age 77 years).
Children:
11. THOMAS BARKER b. ca. 1787-8, d. 1SEP1853 age 76-years, buried Prince William Community Cemetery, Prince William Parish, York Co., NB, m. SUSANNAH _____ (b. ca. 1786).
12. MEHITABLE BARKER b. 17MAR1786, d. ca. 1851, m. Kingsclear Parish, York Co., NB 19SEP1809 EZRA DAY (b. Rhode Island ca. 1760, d. York Co., NB 1836; m. 1st Abigail? _____), s/o Ezra Day.
13. ABRAHAM BARKER, m. HARRIET _____.
14. Capt. JOHN S. BARKER b. Canning Parish, Queens Co., NB (?) 25OCT1792 (ca. 1793), d. Upper Kingsclear, Kingsclear Parish, York Co., NB 23APR1895 (22APR1895 on headstone) age 102 years and 6 months (103-years), buried Prince William Community Cemetery, Prince William Parish, York Co., NB, m. 20JUL1820 RUTH FISKE ESTEY (b. 31MAR1800 (ca. 1800), d. 5JUN1831 age 31 years, buried Prince William Community Cemetery, Prince William Parish, York Co., NB), d/o Amos and Mary (Molly) (Estey) Estey.
15. RICHARD ESTEY BARKER b. 10OCT1794 (ca. 1804?), baptized 27JUL1795, d. Kingsclear Parish, York Co, NB 18APR1850 age 46 (?) years, buried Prince William Community Cemetery, Prince William Parish, York Co., NB, m. Kingsclear Parish, York Co., NB 5NOV1825 MARY (M. A.?) SMITH (b. ca. 1799, d. 1AUG1867 age 68-years, buried Prince William Community Cemetery, Prince William Parish, York Co., NB), 3rd d/o William Smith.
16. MARIA BARKER b. ca. 1795, m. JUL1821 ADAM BENNETT (b. Kincardine, Scotland ca. 1791-2, d. Fredericton 1APR1869).
Alexander Bennet (14) was in Douglas Parish, York Co., NB, working for a “Millman”, Thomas A. Bickwith. The only other persons in York Co. who may have been related were Adam (60) and Maria (56) Bennet in Fredericton with Maria (13). Adam was described as ‘Scotch’ and as having arrived in NB in 1825. Nearby were an Irish couple, Thomas (23) and Grace (20) Bennet having arrived in 1846. There was Amelia Bennet (25), working for John Medley, Anglican Bishop of Fredericton who arrived in 1845 (both of them) when John oversaw the building of the cathedral and became the first bishop. This prompted the creation of Fredericton as a city in 1848 although it did not have a sufficient population. Queen Victoria was not going to have a cathedral of HER church in anything but a city. A widow, Jemima Bennet (55) and her son, John (10), in Kingsclear Parish, York Co., NB, in 1851, were of African descent.
In Canterbury Parish in 1871, Alexander ‘Bennet’ was age 32, and Eliza A. was age 45. Eliza A. d. 16AUG1883 age 58 years.
Adam Bennet was b. Kincardine, Scotland ca. 1791-2, and d. Fredericton 1APR1869. A daughter was Mrs. John McCausland. This was Lucretia Ann Bennett (b. ca. 1829) who m. 29AUG1849 John McCausland.
Another, eldest, daughter, Jane, m. Fredericton 28OCT1841 Wm Cleaveland (William C. Cleaveland) of Sheffield Parish, Sunbury Co., NB. Jane Bennett Cleaveland d. 35 Elton St. Boston, Suffolk Co., MA 25JAN1893 age 72 years, a widow. Her death record gives her as the d/o Adam Bennett and Maria Barker and as born in Fredericton, N.B. Her body was brought to NB by train, probably to Saint John where William had lived.
A William Cleveland m. Portland Parish, Saint John Co., NB 5JAN1837 Eliza Barker. Both were of Portland, so I do not think there is a connection, but the coincidence may be worth noting. A youngest daughter of William C. Cleveland was Carrie Burpee Cleveland (d. Saint John 4JUN1889, m. 6APR1881 James H. Keltie), who lived in Boston. When Carrie married, her father was deceased. Eliza appears to have been the ‘Miza’ Cleveland, widow of Wm. Cleveland, who d. Sussex Parish, Kings Co., NB 20SEP1885 age 68-years.
Carrie Cleveland would appear to be Caroline Cleveland (2), d/o the widow, Jane Cleveland (41) who also had Celia (18), Anne (16), ‘Fredrick’ (14), Jane (7) and Emma. Very nearby lived John Cleveland (78, b. NB) who lived with a daughter, Isabell Getchel (51) and her husband (Lewis C. (50)) and children in Wakefield Parish, Carleton Co., NB in 1861. John drowned in a millpond ca. JUL1868. Isabella Getchell d. 2NOV1893 age 84 years. Lewis C. Getchell d. 6APR1890 age 79 years and 6 months. They lived in Waterville and William c. Cleveland who d. 26APR1860 age 43 years is buried in the Waterville Community Cemetery, Carleton co., NB as are Isabella and Lewis C. Getchell.
Maria E., Jr. m. 1870 James A. S. Mott. In 1882 they went to Winnipeg however he (13OCT1842-15MAY1897) and Maria Elizabeth (d. 27DEC1910) are buried together in Fernhill Cemetery, Saint John.
Alexander Bennett later lived in Canterbury Parish, York Co., NB. He was there when he m. 22SEP1859 Eliza, widow of Daniel Grant. Canterbury Parish was part of Dumfries Parish until 1855. In 1851, Daniel (30) and Eliza Ann (Gray) (28) Grant were Irish but b. in NB. Although given as ‘Miss Jane’ Gray in a wedding announcement, death records of her sons by Daniel Wesley Grant give her forename as Eliza. Alexander, by 1875, was a justice-of-the-Peace in Canterbury Parish for York Co. He also kept the New Brunswick Hotel.
Children:
161. JANE BENNETT b. ca. 1821, d. 35 Elton St. Boston, Suffolk Co., MA 25JAN1893 age 72 years, m. Fredericton 28OCT1841 WILLIAM C. CLEAVELAND.
William may have been a son of _____ and Lydia (Jewett) Cleaveland. Lydia (b. 17NOV1784) was a d/o Daniel and Abigail (Thurston) Jewett.
161. LUCRETIA ANN BENNETT b. ca. 1829, m. 29AUG1849 JOHN McCAUSLAND.
161. MARIA E. BENNETT b. ca. 1838, m. 1870 JAMES A. S. MOTT.
In 1882 they went to Winnipeg however he (13OCT1842-15MAY1897) and Maria Elizabeth (d. 27DEC1910) are buried together in Fernhill Cemetery, Saint John.
162. ALEXANDER BENNETT b. ca. 1838, d. 16FEB1903, m. Howard Settlement, Canterbury Parish, York Co., NB 22SEP1859 ELIZA ANN (GRAY) GRANT (b. ca. 1816 (?), d. 1881; m. 1st ca. JUL1842 Daniel Wesley Grant Grant).
Alexander Bennet (14) was in Douglas Parish, York Co., NB, working for a “Millman”, Thomas A. Bickwith.
Alexander Bennett later lived in Canterbury Parish, York Co., NB. He was there when he m. 22SEP1859 Eliza, widow of Daniel Grant. Canterbury Parish was part of Dumfries Parish until 1855. In 1851, Daniel (30) and Eliza Ann (Gray) (28) Grant were Irish but b. in NB. Although given as ‘Miss Jane’ Gray in a wedding announcement, death records of her sons by Daniel Wesley Grant give her forename as Eliza. Alexander, by 1875, was a justice-of-the-Peace in Canterbury Parish for York Co. He also kept the New Brunswick Hotel.
Daniel Grant m. Dumfries Parish, York Co., NB ca. JUL1842 Mary Jane or Jane Gray. However, in 1851, the family was:

Grant Daniel M Head 30 Irish Farmer Birth
Grant Eliza Ann F Wife 28 Irish Birth
Grant Amaziah M Son 6 Irish Birth
Grant William M Son 5 Irish Birth
Grant Bruice M Son 3 Irish Birth
Grant Eyza M Son 2 Irish Birth

Nearby was the family of Joseph (45) and Sarah (37) Grey, possibly Eliza’s relatives. The progenitors of the family are likely Samuel and Elizabeth Gray of Kingsclear Parish who had children baptized in the Anglican Church between 1797 and 1814.

1798 Aug 24 Gray John 17 Dec 1797 s/o Saml. & Elizabeth Gray Pr. William
1799 Jul 08 Gray Sally 14 Jun 1799 d/o Saml. & Elizabeth Gray Kings Clear
1804 Aug 19 Gray William 17 Jul 1803 s/o Samuel & Elizabeth Kings Clear
1809 Oct 09 Grey James 16 May 1805 c/o Saml. & Elizabeth Kings Clear
1809 Oct 09 Grey Robert 11 Aug 1807 c/o Saml. & Elizabeth Kings Clear
1809 Aug 05 Grey Sarah adult c/o Saml. & Elizabeth Kings Clear
1815 Aug 09 Gray Joseph Morshet 18 May 1812 c/o Samuel & Mrs. Kings Clear
1815 Aug 09 Gray MaryAnn McClain 18 Oct 1814 c/o Samuel & Mrs. Kings Clear

There was also a John Gray who m. in either Prince William or Kingsclear Parish 24AUG1798 Mary Tompkins.

Joseph Gray (ca. 1816) seems particularly associated with Howard Settlement and his family was one of those listed as needing a school in 1844:

60 Joseph Gray 1 4 6 7

This indicates he had a wife, that there were probably 4 children with 6 persons who could benefit from education and that they lived 7 (miles?) from the River.
John Gray of Dumfries Parish left a widow, Mary Gray who m. 27MAR1845 Jabez Lockwood Cronkhite (ca. 1793-1861). The Grant’s in that area are descended from Elizabeth “the widow” Grant, widow of John Grant, who m. 2nd Henry Cronkhite. Her son, Peter Grant, m. Abigail, though to have been a daughter of Jabez Lockwood. This is supposed to have motivated Elizabeth to name a son by her 2nd marriage Jabez Lockwood Cronkhite. So Jabez was a half-brother to the Grant’s. Jabez’ 3rd wife is also given as Mary Newton, widow of John Gray. A daughter of Mary’s 1st marriage is given as Eliza Ann Gray (b. ca. 1816), m. Daniel Wesley Grant (20JAN1817-22OCT1858), s/o William and Ann Maidstone (Hillman) Grant; of a separate (?) Grant family.
17. NICHOLAS W. BARKER b. ca. 1803, d. 4NOV1873 age 70 years, buried Prince William Community Cemetery, Prince William Parish, York Co., NB, m. HANNAH HAZEN ESTEY (b. 13MAY1804 (ca. JUN1804), d. 11DEC1883 age 79 years and 6 months, buried Prince William Community Cemetery, Prince William Parish, York Co., NB), d/o Amos and Mary (Molly) (Estey) Estey.
18. AMOS B. BARKER b. 6JUN1805 (ca. 1806), m. 2nd? MARY DOW (b. ca. 1815-6).

John Barker, Sr. was survived by at least 11 children, but I find only 8, so I am missing at least 3. One, for example, may have been Mary C. Barker (b. ca. 1805) of Fredericton who married 8MAY1845 James M. Wortman (b. ca. 1795) of Kingsclear Parish. They lived very near Thomas Barker (ca. 1788) in 1851 but including her might be too speculative.

Thomas.