To Dundee's point he would have been 19 in 1798, and the fact the children were baptised in Wooler. - Rebekah, Ann and Elizabeth
Perhaps they are the children of Alexander of Wooler (whose first wife Esther Waitman died 1797 buried 21 March 1797 w/o Alexander) and his second wife Mary.
Notes with Esther he had
Alexander 1784, Andrew 1789, John 1791, George 1794