1. Jessie (b.~1913 MO)
2. Charles (b.~1914 MO)
3. Arthur (b.~1916 MO)
4. Mary (b.~1924 MO)

siblings

1. Luther (b.July 1889 MO)
2. Edward (b.~1903 MO)

Research timeline of Kevin Everingham of MI, September 2019;

1900 CENSUS Springfield, Clark, Ohio (sheet 15A, house #339).. "Charles Everingham 41, b.Dec 1859 OH, parents b.OH, married 14 yrs,.. Alice Everingham 30, b.MO, parents b.MO, married abt.1886, mother of 2 children,.. Luther Everingham 11, b.MO,.. Jessie Everingham 8, b.MO."

1910 CENSUS Hannibal Ward, Mason township, Marion County, Missouri (Sheet B2) living at the same dwelling as Lee Morgan who had two other boarders living with him. .. "Charles Everingham 57 b.OH, occ; Carpenter,.. Alice Everingham 38, wife, b.MO, married 22 years, mother of 4 children, 3 living,.. Jessie Everingham 18, son, b.MO,.. Edward Everingham 6, son, b.MO."

1917 WWI Draft Registration of Jesse Everingham, born Feb 5, 1892 at Palmyra, Missouri was working as a clerk at a Candy company in St. Louis, MO. Had a wife and 3 children, was tall, medium build, lt. brown hair, and gray eyes.

This is circumstantial evidence, but I strongly feel like the following is Jessie and family. According to his 1917 draft registration, he had 3 children and worked in St. Louis. The only info not fitting is the fact that he says his father was born in Indiana.
1920 CENSUS St. Louis, St. Louis, MO (Grattan Street sheet 16A).. "J.B. Everingham, 28, b.MO, occ; baker,.. A.M. Everingham, 27, wife, b.MO,.. Jessie Everingham 7, dau, b.MO,.. Chas Everingham 6, son, b.MO,.. Arthur Everingham 4, son, b.MO.. (& two roomers Thomas & Harry Bowler)." further evidence; he named his daughter Jessie, and his first born son Charles.

although his first name is different... this is almost certainly the same family as listed in 1920 & 1940, living on the same street as 1920.
1930 CENSUS St. Louis, St. Louis, Missouri (Grattan Street family #322).. "Joseph Everingham 38, occ; switchman for RR,.. Myrtle Everingham 37, wife,.. Jessie 17, dau, occ: Stenographer,.. Charles 16, son, occ; messenger at RR,.. Arthur 14, son,.. Mary 6, dau. (all born in Missouri, this time he lists his father as born in Ohio, mother born in MO.) "

1940 CENSUS St. Louis, St. Louis, MO, (Hunt Avenue, Sheet 7A)... "Myrtle Everingham 47, b.MO, widow,.. Charles Everingham 26, son, occ; switchman at RR,.. Arthur Everingham 24, son, occ; attendant at filling station,.. Mary Everingham 16, dau."

Lakewood Park Cemetery Affton, St. Louis, Missouri, .. "Jesse B. Everingham (1892 - 1 Aug 1934),.. Myrtle Everingham (b.16 Jan 1893 d.17 Jun 1993).. there is also a Dorris Everingham buried here (1917-1964)."