What role did the nicola sacco and bartolomeo vanzetti case play in america’s fears?

They were apart of of the infamous Sacco and Vanzetti case, which involved and occurred during the Red Scare. [US fear of communists and immigrants spreading their beliefs]

The two people were Italian immigrants accused of robbery, however, no hard evidence was put against them. Despite this, they were still found guilty and even executed due to their ethnicity and involvement with communist groups.
(They were actually involved in the robbery as revealed later by another Italian person after their deaths, a result of his guilt.)

They played a role in America's fears because it was one of the first early events that took play in the Red Scare.

Hope this helps!