Could he be from Carmarthenshire?
No baptism found in Glamorgan Baptism Index CD (1569-1837) (PM-387)
Marriage: 19 Sep 1767 St Athan parish: Charles Bassett of Cowbridge & Catherine Spencer of St Athan. (Glamorgan Marriage Index CD (1569-1837). (PM-391.2)
His father might be Charles Bassett (ID No. 39327) who married Mary Matthew or (ID No. 39329) who married Cate Gwillim. (PM-105)
I, David Attride showed him as son of Charles Bassett (of Cowbridge) because Llanblethian parish death record of 1786 say Charles Bassett (Senior) of Aberthaw and Cowbridge. (PM-178.8)
He was from Cowbridge (PM105)
Note: The tying of him to children Charles & Richard is somewhat hypothetical but based on info from PM-105
To Do: Check Ystradowen birth record for Charles and see if this
Charles was the son of Charles Bassett and Mary Matthew 20 June 1731 or if he was son of
Charles Bassett of Llanblethian and Cate Gwillim of Bonvilston 7 July 1741
Burial: 23 Apr 1786 Cowbridge: Charles Bassett. (Glamorgan Burial Index CD (1569-1841). (PM-388.5 & PM-597)