In the 1851 to 1871 census he says he was born in Ireland
Ref Year: 1871; Census Place: Osnabruck, Stormont, Ontario; Roll: C-10007; Page: 1; Family No: 4.
Link 1851
https://familysearch.org/pal:/MM9.1.1/MWTJ-J9Y
Family search on their family trees give parents as
Gideon Adams 1755-1834 Mary Ann Snyder 1760-1835
But I see there is in the census there is another Joseph Adams in Canada about the same age also born in Ireland
So you need to be sure it’s the correct one.
As your one had a son Gideon Adams born about 1841 (1851census) that to me would be a good pointer.