# These sought their records among those enrolled by their families

"They searched their written genealogical records"

# These sought

"These" refers to the descendants of Hobaiah, Hakkoz and Barzillai.

# but they could not be found

"but they could not find their records" 

# they were excluded from the priesthood as unclean

"the governor treated them as if they were unclean and did not allow them to work as priests"