His father's name is shown as Adain, which may be a typo for Adam; the i and n combined could be an m.
Adam and Caroline's children were born ca 1850-69 and none are listed in the OHDI 1913-1944, which seems unlikely especially for the 3 youngest sons-John, George and Charles if they died in Ohio.
The only son I can find in the 1880 census that could be from this line is Adam SCHEURER, in Ida Village, Monroe, MI: self, Adam H., 32, NY Prussia NY, farmer wife, Mary J., 32, Germany Germany Germany dau, Margaret L., 11, OH son, John Adam, 9, OH son, Henry T., 7, OH son, George D., 4, MI son, Edward, 6/12, MI
Adam's mother's birthplace is wrong but his father's birthplace could be correct if the father was born in the Alsace-Lorraine region. Alsace was ruled by France 1648-1871 and by Germany 1871-1918.
Ida is about 10 miles west of LaSalle, probably closer then cross-country and about the same distance north of the Ohio-Michigan border.