I have become interested in the family name.
It seems to derive from the place Neshchiz (Neskhiz, Nesukhoyshe) in Volhynia. I am attaching a map of hasidic centers from Atlas of Jewish history by Dan Cohn-Sherbok.
Neshchiz is also a hasidic dynasty, founded by R' Mordechai Mi Neshchiz (d. 1800). R' Mordechai's son was R. Isaac b. Mordecai of Neskhiz (1788–1868), author of the book of commentary Toldot Yitzhok.