↑Source:Perley, Sidney. History of Salem, Massachusetts, Vol. 1, p. 131, places this child in the family of John Ingersoll and Mary Coomes, and then says he m. Elizabeth (Symonds) Newhall and had a child. However articles of agreement in the probate of John dated 1695 call Samuel the "only Son of said John Ingersoll", so something is wrong here.
The wording of this baptism record is awkward since the father is named as the son of John Ingersoll, suggesting this is a grandchild of John and Judith Ingersall, and since the son isn't named, the father of the baptized child could John or any of his brothers?
Elizabeth (Symonds) Newhall had her first child 1684 (Nathaniel Newhall Jr.) and there is no good match agewise. But the intentions of John Ingersoll land Elizabeth Newhall were published in Lynn in 1696-7, after the document describing Samuel as the only son of John Ingersoll, so it clearly not a son of John that she married. (Besides the fact that the s/o Samuel was not even 21 at the time of intentions.) Further, an Essex deed (Vol. 21, p. 194) in 1710 shows John Ingersoll of Lynne selling his right to land "which belonged to his father Nathaniel Ingersoll of Salem aforesaid Dec'd or which belonged to his brother Nathaniel Ingersoll of Salem aforesaid". While no wife signs the deed, it seems pretty obvious she married the son of Nathaniel.
The 1678 baptism probably was a son of John's, since a delayed baptism for the son of Nathaniel would be expected to be accompanied by a delayed baptism of Nathaniel's daughter Elizabeth as well, and there is no sign of that.