How to convert Nvarchar column to INT

CONVERT takes the column name, not a string containing the column name; your current expression tries to convert the string A.my_NvarcharColumn to an integer instead of the column content.

SELECT convert (int, N'A.my_NvarcharColumn') FROM A;

should instead be

SELECT convert (int, A.my_NvarcharColumn) FROM A;

Simple SQLfiddle here.