Is the Jennie Day your looking for fit into the following information?
Phillip Day applied for revolutionary pension while living in Smith County, TN., August1832, when he was 70 years of age. He entered the service in 1778 in Caswell County, North Carolina. He died September 9, 1834. His widow Mary Douglas Day applied for pension in Smith County, September 10, 1836, when she was 66 years of age. They were married March 21, 1793. Their children were Sarah Day, born 1794; Thomas B. Day, born 1795; Jenny Day, born 1796; Bethalum Day, born 1789; John D. Day, born 1800; Mary Day, born 1806; Franky Day, born 1807; Franklin B. Day, born 1809; Phillip Day, born 1811; Elizabeth W. Day, born 1813.
The soldier was born April 16, 1762. He married Mary Douglas, daughter of John Douglas. They were both born and reared in Person County, North Carolina.
Source:“Some Tennessee Heroes of the Revolution”, Chapter - Fifth Pamphlet