I have found only two records for Adam Hay-1323. A proclamation of marriage in Abbey Paisley, Scotland (his Parish) and another in Neilston, his wife's parish. Both have the same date, 5 Jun 1790.
The other record for him I found in a Lair Book when I visited the church where he is buried (d.1825). The records mention his son, a daughter, and a grandson, but nothing on his parents.
I wonder if he had any younger siblings? Where were his parents from? What records might be of help?