The Barnett family was in Harrison County, Indiana from about 1815 to about 1840 as evidenced by marriage records. The first was of a David Barnett to Polly Hone 23 Nov 1814 and the latest Barnett marriage in Harrison County was that of a Patsey Barnett to David E. Woods 9 Aug 1838. Keep in mind that Harrison County was much arger at that time.
The first Barnett marriage recorded in Putnam County was that of Thomas Barnett to Elizabeth Evans 29 Nov 1829. I'm not sure who this Thomas Barnett was.
James Otis Barnett was born about 1774 in Virginia. He died about 1850 and is believed to be buried in the Barnett Cemetery.
The first few children of James Otis Barnett and Elizabeth Ann "Betsy" (Keller) Barnett were born in Washington Co., Kentucky from about 1798 to about 1803. Starting with Nancy Ann (Barnett) Killion (born 1805), who is buried at the Barnett Cemetery, the rest of their children were born in Harrison County, Indiana. So the family must have moved from Washington County, Kentucky to Harrison County, Indiana about 1803 - 1805. The last of their children was Lewis, who was born 1817. Lewis was born in Harrison County, so the family moved to Putnam County after that.
Peter Barnett, son of James Otis Barnett and Elizabeth Ann "Betsy" (Keller) Barnett married Sarah "Sallie" Lewis in Clay Co., Indiana in 1828, which appears to be the first Barnett marriage north of Harrison County.