He only had one son David born in Whitby 1-2-1822
On David's baptism William is a Sawyer, so these also appear to be his children:
11 May 1816 (born 10 May) William s/o William & Mary Dixon, Whitby, Sawyer
04 Jul 1820 (born 1 July) John s/o William & Mary Dixon, Whitby, Sawyer
Another possible at Whitby:
05 Oct 1818 (born 2 Oct) Susanna s/o William & Mary Dixon, Whitby, Labourer (Susanna Dixon aged 1 was buried 25 Apr 1820, no parents named).
This one could also be a possible at York, St Denys:
29 Jan 1824 Bennison s/o William & Mary Dickson, Walmgate, Labourer