I think that William's first wife was Alice Thomas, based on birth registrations for William Paterson in June quarter 1927 - mmn = Thomas, and Jessie in 1915. I haven't checked any of the other children shown on 1939 register.
There is a marriage in Worcester RD in December quarter 1911 where Alice Thomas and William Paterson appear on the same page.
A death registration - March quarter 1933 - West Derby RD - Alice Paterson aged 47.