The answer above probably reflected what was on wikitree in 2013. Since then several researchers have investigated and revised this pedigree using info from wills, parish registers and land records, visitations etc.
Amongst Joseph's ancestors (as on wikitree Dec 2020) is indeed a William Pitt son of Thomas Pitt of Bristol who was the son of William Pitt and Helena Haviland. Thomas a merchant of Bristol died in about 1612 when his will was written. The name of his wife is unknown but there is no evidence that is was Priscilla Searle... see below.( though it could be a Mary Pycke, this needs further research. The Pycke family were certainly prominent in Bristol at the time )
The birthdate of his son William is unknown. At present it is given as 1693 but could be a little earlier; he married a Mary Gibbs in 1603
The above mentioned Thomas Pitt of Bristol was the uncle of Thomas Pitt of Blandford, Dorset
. https://www.wikitree.com/wiki/Pitt-82 This Thomas was married to a Priscilla Searle. His son, yet another William who became Mayor of Dorchester .He was buried in 1686 with no surviving male offspring.
