re: "There was a William Adair of Killaisser (Castle ?), Parish of Stoneykirk, Wigtownshire, Scotland, & spouse, Jonnet Cathcart in the riot in Stoneykirk Church as noted in "The Register of the Privy Council of Scotland" Vol. VII AD1638-43."
Perhaps there was a Kirkmaiden connection - (From Scottish Archives : GD117/141 Disposition and resignation by John Cathcart of Cairltoun [Carleton](near Genoch or Little Genoch of Rev. Andrew Adair, not sure of date) to Mr. Hew Cathcart, his son, of a translation of a tack of the parsonage and vicarage teinds of the parish of Kirkmaidine [Kirkmaiden] in the Rynnis of Galloway [Rinns of Galloway]
made to him by John KENNEDY of Creichane [Creechan], 30 December 1617, the said teinds having been set in tack,
with consent of William ADAIR of Kinhilt, the patron, by Mr. John Calender [Callander], parson and vicar of Kirkmaidine, to William McCulloch of Myrtoun, 14 September 1607,
and the tack assigned by the said William ........... to the said John Kennedy, 15 February and 1 July 1617. At Killuquhane [Killochan].26 Jun 1625.
A source noted that John KENNEDY of Creichane was son of William ADAIR. Perhaps from the Scottish Archives search of Creichane (however spelt).