I think the birth year on this profile is wrong - birth 1859, marriage 1857?
Here are some possibilities - 1870 census of Abram, wife Mary E, have son James W, of the correct age. https://familysearch.org/ark:/61903/1:1:MND7-3HJ
Here is a 1909 death record of Abraham T.Turner, at Richmond, parents listed John Turner, Julia Houseman.
https://familysearch.org/ark:/61903/1:1:2W5S-GBC
1865 Richmond Census: https://familysearch.org/ark:/61903/1:1:QVNV-Z3P4
1875 Richmond Census: https://familysearch.org/ark:/61903/1:1:VT85-6XP
1880 Richmond Census: https://familysearch.org/ark:/61903/1:1:MZF6-XP5
1900 Richmond Census: https://familysearch.org/ark:/61903/1:1:MSLR-KHR
Here is information on Mary Eliza:
Death Record: Mary E Turner 11 Aug 1912; parents John Herdman, Mary Ford: https://familysearch.org/ark:/61903/1:1:2W53-H6Q
Burial at Moravian Cemetery, New Dorp, Richmond County (Staten Island)
Mary E Turner : http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=146909553
Abram/Abraham: http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=146909458
1860 Richmond census: https://familysearch.org/ark:/61903/1:1:MC79-R83
Note that on the 1860 census image: https://familysearch.org/ark:/61903/1:1:MC79-RZB, that Julia Turner (W) age 44 is in the the previous household on the same page. and in 1865, that are on consecutive pages. Might be his mother. Don't know if that W stands for widow?