Thank you for your reply, I have only just logged on!
That is very interesting and had never heard of Gellyfrynon farm before, Gelli seems to be used a lot in Llandybie, I have three possibles now, including one which the railway passed through!
I know the Red Lion was there recently for a meal, the building opposite is very old?
In the Parish Register its written Gelli, 1772 to me makes it a possibility, I have been informed whilst on a visit to the library in Aberystwyth that the surname Alexander could have been changed during the patronymic time, something else to look into.
I appreciate very much your reply,