I have much new inf.I don't know if you have discovered this or are still doing research, but here it goes:
Henry Jaycox was married to Sophia GODFREY (she is the daughter of Elisha Godfrey & Polly Barden here is her hx), she had 12 brothers & sisters:
Sophia [Godfrey] Jaycox b. ca 1827 in NY per 1880 Census, m. Henry Jaycox b. 1824, mother of Henrietta b. 1851 and James.
[My note, Henrietta Jaycox m. Cortes Hull b. 1849, Cortes Hull's sister, Alice Eliza Hull b. 1846 in Franklin, VT m. Daniel Tainter, b. March 01, 1839 in NY, son of Polly Godfrey & Daniel Tainter of Jackson Co., MI]. I believe the Jaycox parents are John & Sara Jaycox of NY.
Name Relation Marital Status Gender Race Age Birthplace Occupation Father's Birthplace Mother's Birthplace
Henry H. JAYCOX Self M Male W 56 NY Farmer NY NY
Sopha JAYCOX Wife M Female W 53 NY Keeping House NY NY
James JAYCOX Son S Male W 27 MI At Home NY NY
And, there is this by your research:
Marcus Jaycox, age 23 of Onondaga and Margarette Harth age 18 of Tompkins on 1 January 1856 (record dated at Tompkins) by L.L. Miles, J.P. Witnesses: Henry and Sophia Jaycox of Leslie. D-139[My note, so we know Henry & Sophia [Godfrey] Jaycox were married and I would assume that Marcus is Henry's brother].