Drop the user from Read only Secondary database Always ON server
You can't do this to the secondary only.  Dropping a user modifies the database, which is not possible because the secondary AG database is in read only mode.

You would have to drop it on the primary - then the change will be replicated to the secondary.

From the updated question, it sounds like you're trying to recreate both the login and the user after removing the user from the primary.  

It's hard to tell without seeing the actual T-SQL being executed, but you may have better luck with removing the login from the secondary first, as that is a server level object and thus wasn't removed when you dropped the user on the primary.




  The login and user have been deleted from the primary database, and we are trying to recreate the login on primary. But when we are trying to create the login on primary, it is throwing an error saying it already exists.


I think it's important to clarify something real quick.  A login exists at the instance level, not in any specific database.  You can just connect to each instance and create the login.

A user exists at the database level, and is linked to a login.  To create the user, you'll need to connect to the primary database (whichever instance that happens to be on), and create the user there.  It will automatically be created on the secondary.