I can’t seem to find this anywhere. My parents used it all the time (they were from the Bronx in the 30s/40s/50s) and it’s even in our very own description of the Pit. It’s common enough, but where did it come from?
I’m not quite sure what you mean by that. If you mean it stopped being used as a noun around 1900 then a Google search on “have a beef with” contradicts that. There are plenty of contemporary examples of its use as a noun.