Ancestry. Com has on all the Colgate and Welsh sites that Nancy Welsh is the Daughter of Asaph Colegate. She was born in Huntingdon County Pa. as was her husband. Asaph was living there Both families came to the same area in WV. In the 1850 census Nancy Welsh 60 and Asaph Colegate 85 were in the same household. Nancy names one of her children Rosanna. Asaph's wife's name was Rosanna. Where can I find her name anywhere that shows she is his daughter? The 1800, 1810 census do not show the children's names. He was in the Revolution. Have documentation of that.
Olive Tree Answer: Bob, it sounds like you've done quite a bit of research on your ancestors. You haven't mentioned though if you have looked for documents such as wills, obituaries and other items that might name Nancy as a relative.
Also, have you looked for known children of Asaph? If you can find Nancy sponsoring one of their children at a baptism, or living near them, or witnessing a marriage, you will have more evidence to support the notion that Nancy was Asaph's daughter.
You already have some good circumstantial evidence pointing to a relationship - the naming pattern of Nancy's children; Asaph living with her in his old age... Sometimes we hit a point in our research where all we can do is outline all the documentation we have that supports a theory. It is okay to suggest that Nancy was Asaph's daughter, and present the proof (circumstantial but strong!) that supports your suggestion.