FamilySearch Family Tree, recognizing that it is unlikely that Peter was a son of the 1680 immigrant (as claimed in the Brickey Bible, written no earlier than 1799), has pushed him (and most of his siblings) down a generation (while retaining the 1690 estimated birth year). Whether Peter was a son of the immigrant's son John or of a different son or even of a grandson of the immigrant is not proved. It does appear that the Brickey Bible is missing at least one generation between the immigrant of 1680 and the generation of John, Gerard, Jinsy, Mary and Peter.
An image of the Brickey Bible is in the Memories tab of LBZ7-7LD (FamilySearch Family Tree) (the immigrant).