The Barnum Family (both editions) mistakenly leaves this generation out of the line of descent, showing Joseph's children Justus, Seth, Gabriel and Asher as his brothers, and confusing him with his own son Joseph (1755-1799).
An application for membership in the Sons of the American Revolution, filed by Granville Clark Barnum on 31 March 1932, contains the following statements: The said Col. Joseph Barnum is the ancestor who assisted in establishing American independence, while acting as a member of Captain Hickock's Company at Danbury, Connecticut. While Joseph Barnum's date of birth has not been definitely established, he is mentioned in Richard Barnum's will, dated 14 January 1739, as being the only son of his son Joseph, deceased; and the old family bible which I have, printed in England by "Mark Baset" in 1768, shows that this Joseph died 13 April 1791 and was the father of thirteen children, among whom was Gabriel, referred to as a member of the Connecticut Light Horse Brigade.
In the 1790 US Census for Danbury, Fairfield County, Connecticut there is enumerated a Joseph Barnum who may be this person, as follows:
Joseph Barnum, 2 males over 16 years, 2 females.
A story about Col. Barnum is reported in Susan Hill's History of Danbury, Conn., 1684-1896, published in 1896, as follows: "Porter and a man named Barnum are believed to be the only prisoners the [British] enemy carried away from Danbury. They were taken to New York City and confined in the infamous Sugar House, but Barnum died there from starvation. When found he had a piece of brick in his hand, holding it to his mouth, as if to draw moisture from it to cool his feverish throat....His father, Colonel Joseph Barnum, was seriously affected by the deplorable fate of his boy, and became so full of the spirit of vengeance, that on the next day after getting the news he loaded his gun and started out to avenge himself on sympathizers with the British. Seeing a Tory at work in a field, the half-crazed father fired at him, wounding him severely. He had previously been a professedly pious man, but frequently after the loss of his son concluded his devotions in his family by invoking a curse upon 'old King George and his hellish Crew.'" While it is an interesting bit of local color, this story does not match the birth and death dates of any of Joseph's known sons and is probably apocryphal.
There also exists an account of a Joseph Barnum, prisoner of the British, in the book A Relic of the Revolution by Charles Herbert, of Newburyport, Massachusetts, Boston: Published for the Proprietor, by Charles H. Peirce, 1847. This is an account of American prisoners taken by the British on the high seas and confined at the Old Mill Prison in Plymouth, England. It may or may not relate to this Joseph Barnum. Two paragraphs in the book (from June of 1778) read:
Page 140; Paragraph 29. Joseph Barnum, one of our company, who has been unwell ever since he had the small-pox, more than twelve months ago, has now got the white swelling in his knee, which the doctor thinks will occasion his death, if not cut off; and he is so weak that I fear he is not able to undergo the operation.
Page 143; Paragraph 10. To-day Joseph Barnum, One of our company, and one of the French prisoners that was wounded, had their thighs cutoff. Barnum has been unwell more than a year; he has had a white swelling in his knee.
The birth source shows his surname in error as Burnum.
Connecticut, Deaths and Burials Index, 1650-1934. Name: Joseph Barnum; Death Date: 13 Jul 1791; Death Place: Connecticut; Gender: Male; FHL Film Number: 3084