from Grant Turner's "Turner Family Ancestry"
"For some strange reason, Nathan, one of the sons to William, was not listed in the Doctor’s will. William died at a young age (about 40 years young) on February 15 , 1754. Lydia, William, Daniel and Peter, “my four younger children”, are listed in the will but no mention of Nathan."
==>does not give evidence for Nathan son of William, but location and family names suggest it.
Alternative trees on ancestry.com say Nathan is son of Jacob Turner b.1708 NJ,NJ