What happened when a woman gave birth to a child begotten and born out of wedlock? Did the mother have any legal recourse? If she named the child's father, yes, she did have legal recourse.
Any unmarried white woman would go before a judge of the county court of the county in which the bastard child was born and accuse a person of being the father of the child. Her statement was then reduced to writing and signed.
If the child appeared to be less than three years of age, a warrant was issued, requiring the accused person to be apprehended and brought before a judge of the county court. He was required to enter into recognizance, with good surety, in the sum of $300, to appear at the county court and abide by the judgment of the court.
If the accused person refused to give recognizance, the judge would commit him to the county jail where he would remain there until he gave recognizance or otherwise be discharged by due course of law.  If ordered to pay a sum of money, the father might pay in a lump sum or in installments.
There were cases, however, where the mother of a bastard child never went to court to name the father of her child and it is assumed she and/or her family provided support for the child. The aim of having the father pay for the child was to prevent the child from becoming a charge upon the county.
Bastardy cases are most often found among loose county court papers in the county clerk's office. Among the information given is the name of the mother and the accused father, the date of the child's birth and whether male or female and sometimes where the child was born. Bastardy cases may also be mentioned in the county court minutes, but with fewer details given.
 The Revised Statutes of Kentucky, Approved and Adopted by the General Assembly, 1851 and 1852, and in force from July 1, 1852, Vol. 1 (Cincinnati: Robert Clarke & co., 1867) Chapter 6, Approved 17 February 1858; accessed through Google Books, 2 February 2016.
Published 11 July 2017, Western Kentucky Genealogy Blog, http://wkygenealogy.blogspot.com/