How can I evict people who live in my home and without lease?

I and my relative have rented a apartment in New York. About half years ago, a couple with a little child move into my home. We required them for identity card but they never show us. Thus, we don't know who they are untill now! I am really scare about thoes unidentified people, and I don't know why my mother have compassion for them at begining! We have ask them to leave by both oral and paper(30 days notification). But they threatened us that they would countinue to occupy here for one year. My famliy now are feel uncomfortable to live in our home. We paid everything here and live in a suffering condition. In addition we are force to support their life. Thanks for your time and understanding