Hi,
I think what you’re looking for is Kirk sessions. Unfortunately what Greenvalley says is quite accurate, these are generally for earlier times. Although the Kirk session books continued (in-fact still do today) The practice of investigating Illegitimacies petered during the 1800’s.
Basically the church wanted to have a fathers name before they would baptise a child therefore the Kirk session would convene meat with the parties involved and record the parentage of the child. Because the parish was responsible for caring for the poor this practice was a form of early maintenance for the child. As with all old records many are lost, some never existed and some record limited information however some are very informative and really quite amusing!!
A common punishment was being made to sit in sackcloth at the front of the church and be reprimanded in front of the congregation! Although in most cases this ended before the 1800’s.
These records also hold other informative information about the parish as well as illegitimacies.
The records for most parishes are held in Edinburgh but I would recommend checking the catalogue before you go as some are still held locally. On the whole the records remain un-indexed however if you know the date of birth you wouldn’t necessarily have to read the whole book. Many books have been digitally copied and can be viewed on the computers in the National archives but are not available on-line as yet.
Here are some helpful links:
http://www.maxwellancestry.com/ancestry/kirk.htmOur website explaining a little more about the records
http://www.scotlandspeople.gov.uk/content/help/index.aspx?578More information about the Kirk sessions
http://www.dumgal.gov.uk/historicalindexes/dfskirksession.aspxIndex to Dumfries Kirk sessions
Hope this helps,
Emma