Jesse was the first born child of the second marriage of his father. He had 6 half siblings from his father's first marriage and 4 half brothers from his mother's first marriage. Jesse was about 1 or 1 1/2 years old when his parents and some relatives left Missouri for the wilds of Texas about 1855..
He was 7 years old when the Civil started.
I have yet to figure out how Jesse met his wife, Mary Jane Judkins, because she lived near Rosebud in Falls County. Maybe someday......
He was a victim of tuberculosis. I've been told by Juanita Faucett who said she was told that when he found out he had tuberculosis, he built a room at the back of their home where he lived. This was done to protect his children from the dreaded disease. He died at age 40. It protected them, however, it didn't protect his wife. Mary Jane caught tuberculosis from him and died five years after he did at the age of 39.
Juanita also said that Jesse had red hair and was called "red-headed" Jesse to differentiate him from his father, Jesse J. Dodson.
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From Coryell County, Texas courthouse records:

The State of Texas
County of Coryell, Deed Records, Vol. L., page 250.
Know all men by these presents, that we, Jesse Dodson and wife Mary Jane Dodson of the county of Coryell State of Texas for and in consideration of the sum of Five hundred dollars paid and secured to be paid by Jesse J. Dodson & wife as follows: the receipt of which we hereby acknowledge, have bargained, granted and sold and released, and do by these presents grant, bargain, sell and release unto the said Jesse J. Dodson & wife all of our right title and interest in the place known as the Jesse J. Dodson homestead situated in Coryell County & State of Texas, on the waters of Preachers Creek about fifteen miles S. E. from Gatesville as there has been no division to establish corners this deed calls for our undivided interest in said tract of land. Together with all and singular the rights, hereditaments and appurtenances to the same belonging or in any wise incident or appertaining.
To have and to hold all and singular the said premises unto the said Jesse J. Dodson and wife their heirs and assigns forever, and we Jesse Dodson and wife do hereby bind our heirs, executors and administrators to warrant and forever defend all and similar the said premises unto the said Jesse J. Dodson and wife their heirs and assigns against every person whomsoever lawfully claiming to claim the same of any part thereof.
Witness our hand this the 2nd day of August, A. D. 1877.
Jesse Dodson
Mary J. Dodson

( 14 January 2000. I looked up two of the words mentioned in the above property sale and release in the dictionary to make sure that I typed them correctly as I am not familiar with words of law ) Hereditament means every kind of property capable of being inherited. Appurtenance means something passing as an incident to a principal thing. Patsy )
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• Married: 24 DEC 1876 in Coryell Co, Texas ⁵

1. (John?) Edmond DODSON b: in Flat (Coryell) Texas
2. John (Edmond?) DODSON b: 22 OCT 1877 in Flat (Coryell) Texas
3. Jesse Lee DODSON b: FEB 1879 in Flat (Coryell) Texas
4. Mary Elizabeth "Bettie" DODSON b: 2 JAN 1882 in Flat, Coryell, Texas
5. BENJAMIN FRANKLIN DODSON b: 24 APR 1884 in Flat, Coryell, Texas
6. Wiley Elbert DODSON* b: 20 MAY 1887 in Flat (Coryell) Texas
7. Annie Jane DODSON b: 27 SEP 1891 in Flat (Coryell) Texas

1. Title: Will of his his father, Jesse J. Dodson
2. B.F. Dodson's funeral book, birth and death dates of parents recorded,
   Funeral book of B.F. Dodson, son.
3. Title: Have photo of tombstone
4. Title: Census
5. Title: Marriage Records, Coryell County, Alabama
   Note: Coryell County Texas Court records, Vol D, page 211.