Tough to understand the full story--lots of issues with your post--but you seem to be asking if you can sue because you lost a case. Before trying to sue, (you likely cannot sue the government entity) you should be looking to your rights of appeal.
Recommend you see an employment attorney immediately. After short period of time you may not be able to bring a complaint or suit if you delay.
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I would suggest contacting an experienced employment attorney in Brooklyn, especially if English is not your first language. A face to face meeting might be much more effective at helping you than this online forum. Currently, it is impossible for us to understand what is going on in your case or what evidence you have provided.
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