A sister was put up for adoption and Green doesn't know the whereabouts of two brothers. His mother wandered in and out of his life and he was raised by his grandparents.
"I just want to know where I came from and to know that side of my family history," said Green. "It's hard to describe and it's kind of weird not knowing where the condition of mine came from. People have pointed out the Fugates to me before."
In the 1980s and 1990s, those mountain people dispersed, and the family gene pool became much more diverse. Other relatives, perhaps like Green's paternal relatives, scattered throughout Virginia and Arkansas.
Even today, "you almost never see a patient with it," said Dr. Ayalew Tefferi, a hematologist from Minnesota's Mayo Clinic. "It's a disease that one learns about in medical school and it's infrequent enough to be on every exam in hematology."
In the mildest form, methemoglobinemia causes no harm, and most of the Fugates lived well into their 80s. But in Green's case, his body is starved of oxygen and every organ is affected.
Methemoglobinemia is a blood disorder in which an abnormal amount of methemoglobin -- a form of hemoglobin -- is produced. Methemoglobin cannot effectively release oxygen.
Hemoglobin is responsible for distributing oxygen to the body and without oxygen, the heart, brain and muscles can die.
"I don't breathe very well," said Green. "The red blood cells don't give me enough oxygen."
Green's condition was such an anomaly that hematologists at the Dana Farber Cancer Institute in Boston paid for him to fly East several years ago just to study him.
Most of what is known about methemoglobinemia comes from one doctor's study of the Fugate ancestry in the early 1960s. Dr. Madison Cawein III, a hematologist at the University of Kentucky's Lexington Medical Clinic, drew family charts and blood samples to better understand the genetic disorder.
The most detailed account, "Blue People of Troublesome Creek," was published in 1982 by the University of Indiana's Cathy Trost.
The last in the direct line of Fugates to inherit the gene was Benjamin "Benjy" Stacy, whose skin at birth was "as Blue as Lake Louise," according to doctors at the time. He now lives in Alaska, according to Facebook.
Green is not the only person to wonder if there is a genetic connection to the Blue Fugates.
Jennifer L. Adams Horsley of Hartford, Ind., told ABCNews.com in 2012 that she is certain that her mother-in-law, Amanda Susan Parker Horsley, was descended from the family.
"She was from the upper regions of Kentucky," she said. "Her lips and nail beds were perpetually blue."
"They were like that almost all the time," said Horsley, 62, a retired nurse. "The color depended on when she got upset or was cold. It was so pronounced that everybody thought she was sick."
Parker died at 73 of liver cancer nine years ago, "So we may never know," said her daughter-in-law.
The family presumes that Parker's mother, Mary McCleese Parker, also had the condition. "My grandmother was blue," said Horsley's husband John H. Horsley. "Everyone thought it was real odd."
He grew up in Ohio, but his parents had met in Carter County, Kentucky. The Horsleys said they know of no other children or grandchildren who inherited the gene for methemoglobinemia.