Were might one look to find the parents of William and Richard Barker?
Who are William and Richard?
John (the priest) you say has father, William. Where did that info come from? Do you have Johns marriage cert - if so that should give an occuption for William (to answer Jackies question, and therefore help confirm that the other christenings are siblings of John, children of the same William and Sarah)
So Johns brother, Richard (Jackie found chr) married an Ann, and she is widowed and caring for John the priests children in 1861?
That Richard's father is William, same as John the priests father.
Dont think about trying to get William's father until you are sure that all the later generations are sorted with no assumptions!! One step at a time!