I've found reports on the internet by researchers who claim that many of the children of Osborn and Mary were born in Casey Co., KY. If birthdates found are accurate, all nine of their children were born between 1764 and 1796. Casey Co. was not formed until 1806, and then from Lincoln Co.
According to Kentucky historical marker, the county was named "For Colonel William Casey, early Ky. pioneer and great-grandfather of Samuel L. Clemens, "Mark Twain." Casey born in Va. Came to Ky. in 1779. Built Casey's Station on the Dix River in 1791. Member of Convention, 1799, to frame second Ky. Constitution. Trustee, town of Columbia, 1802. 1813, Presidential elector. Lived Adair Co., died, 1816. County formed from Lincoln."
Elizabeth, Osborn's (variously spelled) daughter was born c1764 and married Christopher Riffe in what was to be Casey Co. on May 9, 1806.
Another state historical marker provides this:
"Christopher Riffe accompanied Col. William Casey (Great-Grandfather of Mark Twain) to Kentucky in 1784. Riffe lived at Bryan's Station, Boonesborough, Logan's Station and Carpenter's Station. He bought 800 acres of land from the Grandfather of Abraham Lincoln. Riffe became the first white settler of Casey County in 1793. He was the first State Representative from Casey County, served seven terms. He fought in the Battle of the Thames (in which Tecumseh was killed) in the Kentucky Sixth Regiment. He was Lieutenant-General of the Kentucky State Militia."
Some Christopher and Elizabeth researchers believe that their children were Peter Bim Riffe and Lehannah Riffe.