All census records are available for free on FamilySearch.org, as are many other records. The 1880 census shows William Sr. living with his mother Anna and grandmother Bridget. Anna is listed as single, and it appears that William was born out of wedlock.https://familysearch.org/ark:/61903/1:1:MWFJ-YXW
And here they are in 1870:https://familysearch.org/ark:/61903/1:1:MZPZ-WGT
Assuming they were Catholic, I would suggest contacting the Catholic Church in Blairsville to see if they have any old baptism or other records that might shed any light on this family.