I'm not related to your Quinn family, but I was looking for a research challenge and I think I found your John Jefferson Quinn.
1910 Choctaw Co. MS
Robert E. Quinn 42 MS
Carrie E. Quinn 42 MS
Pauline Quinn 13 MS (daughter)
Cecil Vaughn 19 MS (Stepson)
John J. Quinn 31 MS (brother)
Juanita V. Quinn 17 MS (stepdaughter)
Virginia Quinn 8 mo. MS (step granddaughter)
It appears that John Jefferson Quinn had an older brother, Robert Estell Quinn. Robert married Carrie. Carrie had been previously married to a man named __ Vaughn. In her first marriage, Carrie had three children: Sidney, Cecil, and Juanita Vaughn. (Sidney was born about 1888 and does not appear in 1910 census with family. She may have died young, or perhaps she was married and out of house by 1910).
Robert Quinn married the widow Carrie Vaughn 8 Dec 1895 in Choctaw Co. MS. (This marriage is recorded as R. E. Quinn - "Cassie" Vaughn but Cassie should be Carrie). After their marriage in 1895, Robert and Carrie had a daughter, Pauline - born 1897.
John J. Quinn was living with his brother Robert in 1910 in Choctaw Co. He had married his brother Robert's step-daughter, Juanita Vaughn about 1908-09. As you can see, Juanita was much younger than John.
John J. Quinn and Juanita Vaughn had a daughter named Virginia Quinn in late 1909.
By 1920, John J. Quinn was in Clay Co. MS.
1920 Clay Co. MS
J. J. Quin 45 MS
Juanita Quin 26 MS can't be sure of ages - hard to read
Virginia Quin 10
J. J. Quin Jr. 8 (28 May 1912 - 17 Oct 1920)
Charles Quin 3
By 1930, they were in Union Co. MS.
1930 Union Co. MS
John J. Quinn m 50 MS
Juanita Quinn f 38 MS (wife)
Charles Quinn m 13
Jessie P. Quinn f 7
Elsie E. Quinn f 5
So, you can see that John and Virginia actually had at least five children: Virginia, John J. Jr., Charles, Jessie, and Elsie. The second child, John J. Jr. died young. I didn't find this family in 1940 census.
John Jefferson Quinn registered for the draft in Clay County, MS in 1918. This W.W. I draft registration shows his birth date as 22 Dec 1878.
The parents of John Jefferson Quinn were Joseph Houston Quinn and Sarah unknown.
The parents of Joseph Houston Quinn were Robert Quinn and Caroline Wilkins.
Many of these Quinns, including your grandfather John J. Quinn are buried in Webster Co. MS. See the following link at "Find a Grave" (just click a name and it will take you to their memorial page)... http://www.findagrave.com/cgi-bin/fg.cgi?page=gsr&GSfn=&...
You will find your Quinn family on Roots Web World Connect here:http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&d...
I hope this information is helpful. If you have any questions or if you want me to search for something else, you can email me directly at firstname.lastname@example.org