These two Kellogg families do not appear to be related. There is a family tree on Ancestry.com that lists Hezekiah Clark Kellogg's Birth 16 May 1805 in Cornwall, Litchfield Co, CT. Death 1886 in Boscobel, Grant Co, WI. His parents are listed as John Kellogg 1777 – 1853 and Mary Clark 1780 – 1856. Hezekiah's marriage 4 Sep 1825 to Elizabeth Catlin 1808-1840. Source citations are not given. The tree traces the Kellogg family back to England in the late 1500s.
These MIGHT be your Hezekiah's census records for 1830 and 1840, before they arrived in Grant Co., WI.
1830 United States Federal Census about Hezekiah Kellogg
Name: Hezekiah Kellogg
Home in 1830 (City, County, State): Catlin, Tioga, New York
Free White Persons - Males - Under 5: 1
Free White Persons - Males - 20 thru 29: 1
Free White Persons - Females - 20 thru 29: 1
Free White Persons - Under 20: 1
Free White Persons - 20 thru 49: 2
Total Free White Persons: 3
Total - All Persons (Free White, Slaves, Free Colored): 3;
1840 United States Federal Census about Hezekiah Kelligg
Name: Hezekiah Kelligg
[Hezekiah Kellogg]
Home in 1840 (City, County, State): Chester, Geauga, Ohio
Free White Persons - Males - 10 thru 14: 1
Free White Persons - Males - 30 thru 39: 1
Free White Persons - Females - 5 thru 9: 1
Free White Persons - Females - 30 thru 39: 1
Persons Employed in Agriculture: 1
Free White Persons - Under 20: 2
Free White Persons - 20 thru 49: 2
Total Free White Persons: 4
Total All Persons - Free White, Free Colored, Slaves: 4