Can I sue my employer for wrongfully accusing me and suspending me even though there is evidence the issue had nothing to do with me?

An employer can fire you in NY for no reason at all, as long as it is not an illegal reason such as discrimination. If the employer accused you of doing something you did not do, and disciplined you and out it in our record, depending on employer you may contact the Union, or complain to the HR department and ask for a proper investigation.