On his mother's Find A Grave Bio, it states that his father was "Will Green", as is shown on his Death Certificate. Death certificates are notorious for incorrect information on everything but the death & burial dates and places. This is a good example of a death certificate informant not having correct information, since Milton Green was William's father, as affirmed in the following life sketch of his father:
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RootsWeb, Updated File June 2009
Entries: 53402 Updated: 2009-06-22 01:47:06 UTC (Mon) Owner: Pam (Hodges) Crain

ID: I16225
Name: Milton GREEN
Given Name: Milton
Surname: GREEN 1
Sex: M
Birth: Abt 1840 1
Death: Abt 1865 in Killed During Civil War - 1
Event: Nationality 1/2 Cherokee Indian 1
Event: Military Union Army Then Quantrila Renegade Band 1
_UID: 206BF0B7235748ECA4F6F187A12194CA1229
Change Date: 27 Jan 2009 at 21:38

Note: "The father of William Jackson Green was Milton Green, a one-half Cherokee Indian. Milton had married Angeline Arnold in Missouri. they had two children, William Jackson Green and Mary Green. William Jackson was born August 4, 1861, in Missouri, during the Springfield Battle. At the time of his birth, his mother could hear cannon blasts from the battle. Times were hard; William J. recalled eating sorghum molasses and cornbread made using ashes for soda. The Civil War began; Milton joined the Union Army. Wife, Angeline, was beaten by a Union Army Commander; Milton vowed revenge. He joined Quantrilla Renegade Band, fighting both North and South armies. Milton was killed, his cabin burned, leaving Angeline widowed with two children. Seven years later Angeline married Christopher Jalle, a Frenchman. He was killed; Angeline then married Martin Smith, a German. She had five children by these marriages."

Matchless Milam, Milam Co., Texas, 1826-1986; from the Killgore Memorial Library, Dumas, Texas borrowed by Ruth Brewer, 7/25/2002.

Marriage 1 Angeline ARNOLD b: Abt 1840
Married: Abt 1860 in Missouri
Change Date: 27 Jan 2009
Children
Has Children: William Jackson GREEN b: 4 Aug 1861 in Missouri During The Springfield Battle
Has No Children: Mary GREEN b: Abt 1862 in Missouri

Sources:
Media: E-Mail received 5 Aug 2002
Abbrev: Ruth Brewer
Title: Descendants of Richard Price I
Author: Ruth BrewerLess
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Contributor:
Harlon