On the 1841 census William TURNER, Whitesmith, born 1811, of Warrington says he was not born in the county.
On the same census William TURNER, Whitesmith, born 1781, of Warrington also says he was not born in the county.
By 1851 William TURNER, the younger of the two whitesmiths has died but the older one with the same daughter but a new wife, says he was born in Chester, Chester.
The son of the William who died early also became a whitesmith so it seems possible that the older man was father to the younger and took his grandson under his wing.
Checking the Cheshire Parish Record Project, I see that William Senior and two siblings appear to be the offspring of William TURNER and Sarah, born 1776, 1781 and 1783 and baptized Chester, St. Mary.
Do you have a marriage for William and Sarah 1775 ish and also William and Ann around 1806? I found his second marriage to Jane on Free BMD.
Thank you for taking time to read this.
Beth