"...the very first application for the house was from an Admiral Croft, with whom he shortly afterwards fell into company in attending the quarter sessions at Taunton"

What are the quarter session at Taunton?

Quarter sessions were courts where suspects were tried for offenses too serious to handled by the Magistrates Court. Judges were on a "circuit" and visited towns quarterly. Mr Shepherd, being a lawyer, was probably there on business. Taunton was the location of the sessions for western Somersetshire.

The quarter sessions were social events, as well as judicial ones. In the book Camilla (by Fanny Burney) it is mentioned that there are balls and breakfasts, etc.