Resources for Genealogy of Dr John Stewart IN Scotland

I've traced my Stewart roots back to Dr. John Stewart (1667-1704), which is as far as I can reliably go. I believe he arrived in America around 1672, because records have him marrying Elizabeth ALBERTI or ALBERTUS (1669-1706)around 1690. I filled in the rest of my family tree according to information I gleaned from Ancestry.com, but there are some major discrepancies in dates in some places, and major connections to Scottish royalty--which would be fantastic if true, but are currently viewed dubiously. Any books or documents that I could review would be very much appreciated.