I stumbled across the newspaper article below giving us another generation in the family of the Bassets of Beaupre in Wales. It lists the children of James Basset. James married someone from Carmarthenshire and had Anthony. Anthony could very well be the ancestor of the #202B Bassetts of Llanelly, Carmarthenshire, as many in that family carried the name of Anthony Bassett.
Cardiff and Merthyr Guardian, Glamorgan, Monmouth and Brecon Gazette, Friday, 15 May 1863