A Somerset County woman died early Sunday after firefighters extinguished a blaze in the basement and first floor of her home, authorities said. The woman, whose name was not released, was found dead about 6:40 a.m. after firefighters doused a small fire in the rear of the first floor and in the basement of the single-family home on West Cliff Street in Somerville, according to Somerset County Prosecutor John P. McDonald. Firefighters found the woman unresponsive inside the house, McDonald said in a joint statement with detectives from the prosecutor’s office and local police. McDonald said fi…