There are some interesting Byfields that were in the river town of Madison during the mid-1800s. Nancy Graham Byfield, the widow of Alford Byfield, lived in Madison with her daughter Catherine "Kate" Byfield. Nancy's husband, Alford, son of Horatio Byfield, died young leaving his widow with a young daughter.
In the 1850 census it appears that Nancy is living back with the Grahams but no daughter is listed with her. There is a young Hannah J Byfield adjacent to the Grahams living with a Guthrie family. Hannah is the right age to be Nancy's daughter.
In the 1860 census, Catherine is with her mother, Nancy, in Madison. Nancy is a dressmaker and has several young girls living with her and working as seamstresses. By the 1870 census, Catherine has been married to John Polasky, widowed a few months after marriage, and is back with her mother in Madison. With Catherine is her young daughter Kate Polasky.
Nancy's daughter Catherine (Hannah J?) eventually married Judge Thomas Woolen. The youngest daughter of Catherine Byfield and Thomas Woolen, Kathryn, in her DAR application, lists her mother as "Hannah Janet Byfield". Also, when Catherine is widowed and living with her youngest daughter, she is recorded as "Hannah" So, it appears that Catherine "Kate" Byfield, daughter of Nancy Graham and Alford Byfield, is the same person as Hannah Janet Byfield. Maybe.