Hi,
There is a tree on Family Search, L6VC-QS3, with William Barnard b 1792 Yorkshire. Married to Elizabeth Mary with one child, John b 1821.
William died 30 November 1867, Peel, Ontario, Canada.
There is a marriage for William Barnard to Elizabeth Wise. 12 Jan 1815, Pocklington, Yorkshire.
Also marriage for William Barnard to Ann Corney. 27 Sep 1813, Aughton with East Cottingwith, Yorkshire.