There are a couple of sources you can use to discover records of illegitimate children in Scotland and some other sources of clues.
Illegitimate children often have their father’s surname in the census, this can often be a clue to who the father was.
If a father refused to support his illegitimate child the mother could take the father to court and extract payment. These records are found in records of Sheriff Courts, you would most likely need to consult the Wigtown Sheriff Court. Fortunately a very kind volunteer has been indexing these records and there does appear to be a record of Jane Clave taking a William Smith to court in 1843.
You can read about ‘Finding Paternity Cases in Sheriff Court Records’ on the Sottish Indexes online guide:
http://www.scottishindexes.co.uk/learningcourt.aspxYou can see the index entry to Jane’s case here:
http://www.scottishindexes.co.uk/courttranscript.aspx?courtid=19004035Another useful type of record are the Kirk Session records. Sadly few of these are indexed or available to access online/outside Scotland. When you are able to access them, however, they are very useful. The church would often investigate cases of illegitimacy within their parish, and this would almost certainly happen when a mother wanted her child to be baptised. The church would also be keen to make sure that fathers paid for their children. The Sheriff Court records and the Kirk Session records can complement each other, both providing information from different perspectives.
The National Records of Scotland (NRs) held most Kirk Session records until recently and have digitally imaged all the records they then held. All can therefore be accessed at Scottish archives with remote access to the NRS or at the National Records of Scotland itself. I believe there is a plan to make these valuable documents available online but I’m not holding my breath!