There's a klezmer tune called Koilen ("Coal"), dating back to at least 1919, sounding amazingly close to Bella Ciao. How and when the tune got from klezmer to Northern Italy, or from Northern Italy to klezmer, is a mustery to me.

Here's a recording, with links to discussions of the two pieces. The recording is an instrumental, but there are also Yiddish lyrics going back to (at least) 1919, at https://www.loc.gov/resource/ihas.200182349.0/?sp=1

Probably worth reading the discussion here: http://riowang.blogspot.com/2008/12/bella-ciao.html