I afraid that unless they fired you for a reason that violates New York law (such as age discrimination, or sex discrimination, or race or religious discrimination, etc. or Federal law (such as being fired for union activity) there really isn't much that you can do unless you have an employment contract or are represented by a union. The reason is that most NY employment law relationships are what is known as "at will". This means that you can work for an employer, or not, your choice. In turn, the employer can hire or fire someone for any reason or no reason whatsoever.

The only exceptions to this are: 1) If there is an employment agreement or contract (which governs termination); 2) If there is a union or collective bargaining agreement (which governs termination); 3) If there is an employee handbook or other official policy statement (which governs termination); 4) If discrimination is a factor (there can be no termination for reasons of race, religion, age, disability, sex, national origin).

A employment attorney should advise you. See a Brooklyn area employment attorney as your firing may part of a pattern of illegal conduct -- which the lawyer probably knows about -- that violates NY or federal law. An employment lawyer in Brooklyn can help in that case.