The Barnum Family calls him Nathaniel B. Barnum, and gives him a birth year of 1773. The reference appears to be an error, probably referring to his son, Nathaniel Bisco/Brisco Barnum.
In The Old United Empire Loyalists List, Centennial Committee, Toronto, Canada: Rose Publishing Co., 1885. Appendix B appear the following names:
Barnum, Nathaniel - H District - Dead-a Lieut.
Barnum, Nathan Bunnel - London District - Formerly soldier in 3rd Battalion of Delaney's. O.C. 26th January, 1808.
Barnum, Levi - Sergeant King's Rangers.
This may be the Nathaniel Barnum referred to in the list.
At the conclusion of the Revolutionary War, with the severance of the Colonies from Great Britain, the Loyalists, who supported the British Crown, began to move north into what is now New Brunswick, Nova Scotia and Upper Canada. This list is the official register of families and individuals who had adhered to the Unity of the Empire and joined the Royal Standard in America before the Treaty of Separation in 1783. Persons falling into this category were given a mark of honour by the British Crown and known as United Empire Loyalists. Much of the present population of Upper Canada can trace their descent from these early pioneers, making this record of interest to anyone with ancestors in those areas.