Speculation:
could be the son or relative of:
Jonathan Everingham(b.1764)

1. Emeline L. (b.~1817)
2. Elizabeth Catherine (b.~1819)
3. Rowena (~1821)
4. Maria T.
5. Martha H.F.
6. Charles W. (b.~1825-30)
7. Ladorna Jennie
8. Warren (b.~1830)
9. Frances (b.~1833)

currently unknown

¹Information from the records of Ann J. Everingham.
²Information & speculation by Tom Phillips, of PA.
³Ezekiel appears in the 1820, 30 & 40 CENSUS of Steuben County, New York. (name sometimes listed as "Ezkel") By the 1860 Steuben Co. CENSUS, widowed wife Catharine Evingham is listed with the "H.L. Jones Family".
⁴Ann's other information says: according to the 1860 CENSUS listed above, Frances, dtr of Ez & Cathrine was born abt 1833, Warren, son of Ez & Cath was born 1830 & married Mary, born 1826"

Research below from Kevin Everingham of MI, 2004-2009
"Based on my research of Sgt. C. Warren Evingham"... I think it is possible that #6 Charles W. listed above, and #8 C. Warren may be the same person."

The 1817 Dansville record below is the earliest record of Ezekiel (that I know of)
1817 Dansville Masonic Lodge #306, at 68 Elizabeth Street, Dansville, NY...according to their Lodge history, On November 15, 1817, a petition was formulated for the organization. The following names were affixed to this petition: Abel Baker, Neil Boyden, Elihu Warner, Ebenezer Bullock, Timothy Atwood, Amaziah Hammond, Ezekiel Evingham, Warren Patchin, William Lemmon, Arad Sheldon, Nathaniel Brayton, and Samuel Stillwell.

1820 US CENSUS Dansville, Steuben County, NY.. "Ezekial Everingham", on the next page is Jonathan Everingham a possible cousin or brother., also listed in this census is; Daniel Shaw

1828 Livingston Journal, Geneseo NY, Oct 1, 1828,.. "Ezekiel Everingham" is listed as having a letter at the Dansville village post office. this info is of little value except to establish location.

1840 US CENSUS Dansville, Steuben, New York (Page 13).. "Ezekiel Everingham, 1M 5-10, 1M 10-15, 1M 40-50, 1F 5-10, 2F 10-15, 1F 15-20, 1F40-50."

1842 Saint Peters Cemetery, Pfaff Road, Steuben County, New York.... Ezekial Everingham 1791-1842. Show Ezekial died 4 March 1842, age 51.

1850 CENSUS North Dansville, Livingston, NY (Aug 22, 1850, family #344) .. Thos Squires 30, lumber man,.. Maria Squires 25,.. Chas Squires 11/12,.. Cath Evingham 58, b.MA?
no idea if the 1850 census is the right Catherine... did daughter Maria marry T. Squires?

1855 STATE CENSUS Dansville, Steuben County, NY (Page 22, June 1855).. "#194- Henry L. Jones 34,.. Roana M Jones 34, wife,.. Hananda 3, dau,.. Fany 1,.. Patrick Donnelly 21..
#195- Major Jones 24,.. Jenie Jones 22,.. Jennie Jones 11/12,.. Catherine Evingham 60, b.Ma"
1855 in a State Census of North Dansville, Livingston, NY,.. there was a Thomas Squires 33, and wife, Theadotia M. Squires 29,.. and child Helen J. Squires 2. Is "Theadotia", Maria's middle name?

1860 CENSUS Dansville, Steuben, NY ... H.L. Jones,.. Roena Jones,.. Celestia Jones 8,.. Fanne Jones 6,.. Roena Jones 2.,.. Catharine Evingham 60, b.NY.

1870 CENSUS Dansville, Steuben, NY, June 1870 ... (Page 21 family #170) ... Catherine Evingham 77,.. Frances Carlton 40, no employment,.. Casius Carlton 11,.. Eliza Healy 50, no employment,.. Katie Healy 7. (all born in NY, Katie born in MI.)

1875 STATE CENSUS S. Dansville, Steuben, NY (Page 39, family #312) ... Henry L. Jones 54,.. Roena M. Jones 54,.. Selesia A. Jones 23,.. Fanny T. Jones 21,.. Katie R. Jones 17,.. Effie M. Jones 13,.. Chas C. Jones 11,.. Catherine Evingham 83, b.MA.

1880 CENSUS Dansville, Steuben Co., NY
Henry L. Jones, 59, farmer, born in NY, Rowena Jones, wife, 59, born in NY, father born in NJ, mother born in MA, Kate R. Jones, b.NY, 22, teacher, Effie Jones, b.NY, 18, Charles C. Jones, farm laborer, b. NY, 16, Catherine Everingham, mother-in-law, 89, b. MA.