January 8, 1935
In Tupelo, Mississippi, shortly before dawn, in a two-room house built by her husband and her brother-in-law, Gladys Presley gives birth to identical twin sons. The first, Jessie Garon, is born dead. The second, Elvis Aaron, is born alive and healthy. Elvis would be their only child.
http://www.elvis.com/elvisology/bio/elvis_1935_1957.asp
Similarly, there is some slight confusion regarding the spelling of Jesse Garon's name. Most reliable resources have the spelling as Jesse. However, near the graves of Elvis, his parents and his grandmother at
Graceland is a marker the family placed in memory of Elvis' twin, but the spelling is Jessie for reasons we have yet to determine. Jesse Garon's actual grave site is in Tupelo, MS where it has always been, but it remains unmarked by a tombstone. Lack of money in the family's early years was likely the reason. Then, once Elvis became wealthy and famous, the grave, which is in a public cemetery, remained unmarked most likely in the interest of privacy. Because of the spelling on the marker at
Graceland, we tend to use the spelling Jessie to avoid confusion.