I have made an assumption that these are the parents of William B. Turner, because they were all born in NY, and all are living at Becket, MA, in the censuses.
In the 1850 and 1860 Federal Censuses, John & Sarah Turner are living at Becket, Berkshire Co., MA.
In 1870, John is living at Granville, Hampden Co., MA, with Samuel & Sarah Brooker and family. Sarah Brooker is John's daughter. I assume his wife Sarah must have died.
John's death record at Granville identifies his parents as David & Susan Turner. This may or may not be accurate, depending on the knowledge of the informant at the time of his death. The 1800 Federal Census lists a David Turner at Schodack, Rensselaer Co., NY; data shows two white males under age 10, among other categories. There are several other Turner families listed for that area of New York State.