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I hope this message finds you well, present circumstances excluded. I am assuming that you received a ticket under the linked code section: http://codes.lp.findlaw.com/nycode/ADC/16/1/16-118.
There is no mandate to appear in court over a littering ticket in NYC. They have to give you a court date by law since they are issuing a citation. This goes to the due process requirement that you are given a day in court. You should be able to pay the fine either over the phone or by certified check or money order. Unfortunately, this means that you will have to be able to get someone on the phone to properly identify the court assessment and cost of the citation (it used to be around $180.00, but that might have changed).
In summary, if you are not going to contest the validity of the citation or ticket, you simply need to find out the amount owed (which will be the hard part) and then pay the fine. Be sure if you mail in payment that you note what the payment is for by way of either including a copy of the ticket or a note that specifies the ticket number.
Let me know if you have any other questions or comments. Best wishes going forward!