Winters Family

This is not very likely to work. This is too late for bastardy bonds to apply (after 1834).  There is also confusion over the source of poor relief – it was (pre 1834) dealt out by the Overseers of the Poor, not the church or vestry.  The Overseers handled allowances for single mothers/their babies, collected from the father.
After 1834, ordinary poor relief came (ultimately) from the Board of Guardians of the Union of parishes, and was physically paid over by the Relieving  officer. But this did not usually apply in filiation cases. There possibly could be a record of the birth in a workhouse. Not many Workhouse records for the Unions exist in the early years.

In any case, maintenance had to be applied for from the Petty sessions, so by far the best source is newspaper reports of the proceedings of magistrates, which could well name the father. The court proceeding should be reported in the local newspaper within about 3 weeks of the child’s birth – assuming that the father was not careful and generous enough to pay up a lump sum without prompting, thus keeping his name out of court. If he paid something on account, or promised to pay and stopped doing so after a while, then there could be a filiation case later, even after a matter of a couple of years.