I am trying to locate the parents of a William A Davisson b. abt 1856 0r 1857. The information you have posted would seem to fit. Recently, on a trip to Indiana,I had a little bit of time to fill before my flight home, so I went to the state library in Indianapolis and got a copy of William A. Davisson's marriage certificate. I also got a copy of a land purchase dated Jan 12, 1878 in which Wm A Davison bought land from George W. Balsley. It is recorded as a quit claim deed, which tends to indicate a close relationship, for example that he was family.

Do you have any information on the William Davisson who was three in 1850?

William A Davisson shows up in the 1880 Census for Prairie, Kociusko County as follows:

Name: William A. Davisson
Home in 1880: Prairie, Kosciusko, Indiana
Age: 23
Estimated Birth Year: abt 1857
Birthplace: Indiana
Relation to Head of Household: Self (Head)
Spouse's Name: Mary C.
Father's birthplace: Ohio
Mother's birthplace: Ohio
Occupation: Farmer
Marital Status: Married
Household Members:
Name Age
William A. Davisson 23
Mary C. Davisson 22
Perry E. Davisson 3
Adaline Beckner 24

I believe that Adeline Beckner, is actually Mary's sister.

Unfortunately there is no copy of the 1890 census. By 1900, there is a William A and family living in Nebraska. This could be him, as I know for a fact that William's son Perry moved there, however not positive. Would appreciate any further information you may have on this family.