I searched ScotlandsPeople old records today for births or baptisms in Scotland. My search terms were: surname begins with "gre"; first name begins with "arch"; sex: male; dates: between 1680 and 1715; place: all of Scotland (not just Dunbar). Amazingly, there were only 14 "hits" and I've listed them below (minus eight obviously incorrect names: Greere, Grege, Gregg, Gregory, Greig, Grierson, Greive):
1 08/04/1694 GREEGE ARCHIBALD NATHAN GREEGE/ M BARONY GLASGOW CITY CITY/LANARK 622/00 0010 0041
2 31/01/1685 GREENFEILD ARCHBALD JAMES GREENFEILD/MARGREAT DENHOLME FR10 SPOTT /EAST LOTHIAN 720/00 0010 0007
3 14/10/1682 GREENFIELD ARCHIBALD ALEXANDER GREENFIELD/MARY WAIT FR739 M HADDINGTON /EAST LOTHIAN 709/00 0020 0337
4 20/12/1688 GREENFIELD ARCHIBALD ANDREW GREENFIELD/AGNES DENNIM FR16 SPOTT /EAST LOTHIAN 720/00 0010 0017
5 06/04/1712 GREENFIELD ARCHIBALD JAMES GREENFIELD/ISOBELL GREENFIELD FR51 SPOTT /EAST LOTHIAN 720/00 0010 0078
6 24/11/1692 GREENLEAVS ARCHBALD ARCHBALD GREENLEAVS/ DUNBAR /EAST LOTHIAN 706/00 0010 0086
Note that no. 6 above is the person most researchers believe is ARCHIBALD GREENFIELD of Dunbar, East Lothian, Scotland, bap. 24 Nov 1692, who came to America and married HANNAH STARR, SARAH BACON, MARY PLATT, and MARY GAUTIER. But this child's last name is GREENLEAVS (GREENLEAVES, not Greenfield).
Could it be possible that our Archibald Greenfield is child no. 2 above? He was born 31 Jan 1685 at Spott in East Lothian. This makes him only seven years older that child no. 6. It is also interesting that Archibald Greenfield of Salem named his first son JAMES. Coincidentally (?), child no. 2's father is James. Archibald might have named his firstborn son after his father. Child no. 2's mother was MARGREAT DENHOLME.
At this point, I haven't discovered any evidence, support, or source that proves Archibald Greenfield's parents were Archibald Greenfield and Christian Bookloss of Dunbar, East Lothian, Scotland. Again, I welcome comments and discussion.
Sincerely,
Jan