I found a 4 year old child, George, living in a household of a old 54 woman, Atlanta, in 1860? Could she be his mother? Where was he born? http://"United States Census, 1860", database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MC76-19X : 18 February 2021), Jedediah Bonney, 1860.
Edited: after 3 attempts to copy the link I can not make the connection. Maybe someone can find it by the information given. Jedediah Bonney-470 is the supposed father.
It looks like he is a grandson.
The family is listed in the 1865 Census of Ellisburg, Jefferson County, New York, incorrectly under the name Barney:
http://"New York State Census, 1865," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QVNV-44KR : 8 March 2021), George D Barney in household of Jedediah Barney, District 02, Ellisburg, Jefferson, New York, United States; citing Census, p. 4, citing multiple county Clerks; Warren and Lewis County Board of Supervisors; multiple counties in New York; Utica and East Hampton Public Libraries, New York.
Atlanta is called wife and George grandson.