I have had trouble locating a Jon Barrett, thru census and county records and a little help from information online, the following is what I have been able to piece together.
1 William\Jon Barrett abt 1819 Ore Hill, Armstrong Co., PA-c 1878
--+ Maria Austin c 1822 PA dau of Gaird Austin and Martha
--m 1842 PA
----2 James J Barrett 1841
----2 Martha Barrett 1843
----2 David Barrett 12-1-1845
----2 Daniel Barrett 8-5-1848-10-8-1911
----2 Rachel Barrett 1851
----2 John Franklin Barrett 6-27-1854-7-11-1910
----2 Thomas Barrett
----2 George Barrett 1865
----2 William E Barrett c 1860-1934
------July 3, 1889 Jamestown, NY
------m Annie McCool 1868-1943 dau of Thomas McCool & Margaret Neal
--------3 Emory Ward Barrett born abt 1892 died abt 1960
----------m Mar 17, 1915 at the bride's home in Tionesta, Forest Co., PA
----------+ Elizabeth Porter April 4,1893- August 10, 1934 Mansfield, OH Dau of E. M. Porter & Anna L Butler
------------4 Ruth Barrett 1918
------------4 Emory Ward Barrett 1923 Oil City,PA- May 29, 2000 Riverside Hospital, Columbus, Ohio buried Reserrection Cem.
--------------+ Mary Jane Antoinette Soehnlen
----------------5 Barrett
------------------+R Corrigan
----------------5 Barrett
------------------+ Marcum
------------------+ ?
----------------5 Barrett
------------------+ Fries
--------3 Edward Dewitt Barrett Mar 25, 1894 Merionville, PA -Jan 1,1966 Warren, PA.
----------+ m. Jan 1, 1916 Polk, Pa Grace Alvenda Kaltenbach 5-8-1893 Grove City, PA - Nov 30, 1971 Warren, PA
------------4 Charles Edward Barrett
--------------+ Marge Champion
----------------5 Barrett
----------------5 Barrett
--------------+ Margaret Jean Paterson
----------------5 Barrett
----------------5 Barrett
------------4 Katherine Barrett
--------------+ Archie Phillips
----------------5 Phillips
----------------5 Phillips
----------------5 Phillips
----------------5 Phillips
-------------4 William Barrett
---------------+ Elsie Lundmark
----------------5 Barrett
----------------5 Barrett
----------------5 Barrett
----------------5 Barrett
--------3 Florence Barrett
----------+ Robert Watson
------------4 Roberta Watson
------------4 Pauline K Watson
--------------+ Clifford Knowlton
----------------5 Knowlton
----------------5 Knowlton
----------------5 Knowlton
--------------+ Kenneth L Peterson
--------3 Dell Barrett
--------3 Allen Barrett
--------3 Margaret Barrett