Thanks Francis, but what/whose marriage register? And why would the birth show in the
marriage register of William and Jane?

As I mentioned I can find no marriage record of Joseph Clarkson and Isabelle Kelly.

The link to Gick of Cordeman can only be via Isabelle. So, I am stuck, if it is not Jane(Gick/Jick) and William Kelly.

You say there are children shown in the IGI but their names are Jane, and Elizabeth. Jane would seem logical, especially if she is the first daughter, as that is her mother's name.

Thanks again