I do not think that Gershom & Prudence had a son Daniel W. b. ca. 1812.
Gary Beam quotes Roberts' History of Remsen:
Gershom HINCKLEY (28 Aug. 1763, Stonington, NL, CT - 20 Feb. 1848, bu. Liverpool, Salina Twp., Onondaga, NY) m. 1788/9, Prudence TENNANT (8 Aug. 1770 - 3 Apr. 1852, bu. Liverpool), dau/o Caleb TENNANT of Glastonbury, CT.They had(in New York)
Daniel W. HINCKLEY, b. 11 Feb. 1790, d. inf.
John, b. 17 Jan. 1791, m. Rhoda BALL
Anna, b. 7 Feb. 1793, m1. French FAIRCHILD; m2. Zebina BALL; m3. Jacob STAFFORD
Caleb, b. 20 Oct. 1794, d. inf.
Catherine (15 Jan. 1798 - 11 Jan. 1829) m. 1819, Mile[s] MITCHELL
Harriet (19 May 1801 - ca. 1838) m. Evert DYCKMAN
Daniel, b. 30 Nov. 1803
Henry R. (20 July 1805 - 19 Jan. 1852, bu. Harwick, aka Old Van Antwerp Cem., Antwerp Twp., Van Buren Co., MI)
Hiram, b. 10 June 1807, m. Sarah M. SMITH
Tennant, b. 13 Jan. 1810, m. Malonia STILES
Moses, b. 20 Jan. 1812, m. Maria Van ALSTYNE
Stephen, b. 29 Mar. 1814, m. Emily SEARS.
Census of 1850 shows Daniel W. HINCKLEY of Summit Co., OH, with wf. Elizabeth & 3 ch.
In 1860, they apparently were incorrectly listed in Elyria, Lorain, OH, as PECK:
Harmon, 55; Lydia, 37; Daniel, 57; Eliza, 32; Anna, & Maryette.
Ridgeville, Lorain, OH, 1870,
PECK, Harmon, 65, Lydia, 58; with
HINCKLEY, Eliza, 42, Anna, 14, & Marietta, 12.
Marriage license, Summit Co., OH, 17 June 1844, Daniel HINCKLEY & Eliza BRANNAN?The erroneous birth year may have come from this document, with someone misinterpreting Daniel's statement that he was over 21. Her maiden name is hard to decipher, some have said BRANNER & some BRANSON.At Boston, Summit, OH, 1850, there were a Robert BRANON, 50, & Mary, 55, VA.
Never give up!