Is this where you file a small claims suit against the former landlord

If the person or company you are suing is located in the 5 west towns of suffolk, you may use any of the 5 civil district courts. See https://www.nycourts.gov/legacypdfs/courts/10jd/suffolk/dist/pdf/DC-283web.pdf And http://ww2.nycourts.gov/courts/10jd/suffolk/dist/smallclaimsbook.shtml

Try 5th district Court for that....that's where I went to do the same thing...