THere is a WIlliam, son of James Auchinleck of Kenmay and Janet Hepburn, [1] but there is nothing that ties him to this William.
Sources
↑Paul, James Balfour. "The Scots Peerage : founded on Wood's ed. of Sir Robert Douglas's Peerage of Scotland; containing an historical and genealogical account of the nobility of that kingdom", Edinburgh: David Douglas, 1905, Vol. II, Archive.org,
p. 150