Carluke Session records. Several entries on pages 342 & 343 relating to Alexander's birth and parentage. "8th May 1791 Betty Morton, presently residing in the upper town of Cambusnethan, confessed herself with child and gave up John Stewart, coal-hewer at Gillhead in the parish of Cambusnethan as the father of her child and said that the child was begot when she was a servant in this parish".
John was, after a couple of attempts, made to appear before Carluke Session, where he first denied being the father and then finally admitted to "uncleaness" with Betty!
In my opinion, Betty must have been born in Carluke parish, if she she had been born in Cambusnethan, given the fact that she was, at the time of the entries made in the Carluke records, actually living in Wishaw (Cambusnethan parish) she would have been brought before Cambusnethan Session. I noticed there was a couple of entries for parochial relief in Carluke Session records for "Betty Morton in Law" (Law is a village, very close to Wishaw but in Carluke parish) this may or may not be her, it could even refer to her mother or grandmother but, it may be a clue to her origins, it can't be ignored until it can be discredited.
John Stewart was a coal miner at Gillhead, this is in modern-day Wishaw, an area in the Dimsdale part of the town, about 2 miles from Law village. It gives us a clue to his residence and, perhaps more can be found?
I'll have a look through any records I have for the name Stewart at Gillhead.