I googled “New York residential lease.” I came up with countless web sites that show what they claim is a standard New York residential lease. They are not all the same, but the couple I looked at both had a clause similar to this:
So I don’t know whether there is a general rule in NY small claims court about recovering attorney costs, but it appears that in a typical lease, the tenant agrees to pay the landlord’s attorneys’ fees. So I would guess that if the defendant has agreed to pay attorneys’ fees, that agreement is enforceable in a NY small claims court.
In Ohio small claims courts, attorney fees are not held against the $6k maximum that you can otherwise win (for many years it was just $3k). Costs such as filing fees, witness fees, photocopying costs, etc. can be recovered. Pain and suffering, or lost wages for time spent in court, typically cannot.