Green B. Jameson is often listed to be of different parents, mostly as a son of a Benjamin Jameson of New Jersey. This is not correct.
There does not seem to be any question about Green B. Jameson as he exists in Texas, either to when and or where. There is also no question that the Green B. Jameson who died at the Alamo was born about 1805-1807 and in Kentucky. There is however, an issue about Green B. Jameson's parents, siblings and ancestry.
The Green B. Jameson that lived in Texas in the 1830's and died during the battle at the Alamo on March 6th, 1863, was Green Berry Jameson, who was born in October of 1805 in Kentucky, the son of William and Jane Jameson of Barren County. He was one of eight known children, including: Willis Lea Jameson (1793-1853), Gillian S. Jameson (1797-1856), Julia Ann Jameson (c1809-?), Christopher Hawkins Jameson (c1810-a1834), Desting Jameson (bc1811-?) and Eloise T. Jameson 1812-1873). His grandfather was John James Jameson, also of Kentucky, who had died there in Fayette County in 1805.
There are numerous, contemporaneous letters and documents, most of which are already in various Texas libraries, historical and military repositories, as well as other entities, that support and substantiate these facts. The oldest of these is probably a letter written by Green Jameson's brother, Christopher Hawkins Jameson, dated February 3rd 1834. In this letter C.H. Jameson writes his brother Green Jameson, inquiring about moving to Texas to join him. He also mentions several members of their family, by name and with various important dates. Furthermore the information in this letter is consistent with and supported by, various separately existing official Kentucky documents, including land purchases, marriage records and other items. This one letter alone, ties everyone together, including Green, independently of anything Texas.
Then there is the matter of the Texas land granted to Green Jameson for his service at the Alamo, by way of an act by the Texas Congress in 1837. This donated land was awarded to "his heirs, executors, administrators, or their assigns," Several documents, including legal proceedings in the Texas Courts in 1851, various letter and correspondence and the ultimate distribution of this land to Mary (Jameson) Nuckols, Green Jmesons sister, in 1874, is absolute further proof of his direct connection with the known and verifiable family of William and Jane Jameson, of Barren County Kentucky. Mrs. P. Nuckles (sic) - Mary Sarah [Jameson] Nuckols, ended up as the sole heir to Green B. Jameson's entire estate, which consisted of property throughout the territory: Marion and Milam Counties, Texas. Semiramis Jemison, Mary's daughter, was heir to Green's property, after her mother's death. More details here
Green Jameson's nephew, John J. Jameson, gave an affidavit in December of 1900 in Davidson County, Tennessee, where he was living at that time. This affidavit is well detailed account of the family, based on his personal knowledge, family stories and a family bible he possessed. The purpose of this affidavit is unclear, although it almost certainly had to do with the issue of his uncle's estate and can now be found amongst the Green B. Jameson Probate Records at the Alamo. Library. Regardless of the purpose for this affidavit, it's contents are the most extensive and detailed account about this family and clearly show that the Green B. Jameson born to William and Jane Jameson of Barren County Kentucky is undoubtedly that same Green B. Jameson who fought and died at the Alamo in 1836
Surprisingly, and in spite of this clear evidence, there is considerable modern day literature that lists this Green B. Jameson as the son of entirely different parents and grand parents, namely that of a Benjamin Jameson of New Jersey. Regrettably, this association is never explained, referenced, sourced or documented in any way. What evidence there is of this Benjamin Jameson of New Jersey seems sparse and unproven and never has any reference to a son named Green or anything close. Exactly how this Benjamin Jameson got attached to the Green B. Jameson of Alamo fame is a mystery, and is incorrect. Ironically, most of the details and documents proving Green B. Jameson's family and heritage are housed in Texas, some even at the Alamo.
 Date derived - based on a ship's record of New York Passenger lists, 1820-1957, showing Green B. Jameson, lawyer, departed Vera Cruz, Mexico, on the ship Congress, arriving at the port of New York on 23 Jan 1832. It gives his age as 26 years, 3 months, which would make his birth about October 1805
 Some believe there were nine children, including an Emily Jameson (b.c1800-d.1831), based on an 1834 letter written by Green Jameson's brother, Christopher Hawkins Jameson. The Emily mentioned in that letter is however, much more likely the second wife of Willis Lee Jameson.
 Original letter held by the County Clerk of Brasoria County, Texas, as part of the Green B. Jameson Probate file # 274 - facsimile here - transcription here.
 Facsimile here.
 The Southwestern Reporter, Volume 21 - 1893, West Publishing Company
 The Jameson Perspective - Scott Jameson
 Daughters of the Republic of Texas Library at the Alamo, Vertical File - Facsimile here. Transcription here.