You should not have even been ticketed unless there was a legitimate basis for demanding to see your identification. As far as I know, there must be some basis for making such a demand and there is no requirement to show a photo identification to the police. If there is such a requirement, then we're already living in a Nazi state as far as I'm concerned and something has to be done about it.
Consult immediately with an experienced criminal defense lawyer in your area and fight it wholeheartedly.
This answer is not intended to form an attorney/client relationship and any answers do not constitute direct legal advice and should not be followed unless and until you have spoken with an attorney of your choice.
What statute does the ticket accuse you of violating? I am not aware of any law that requires someone to carry id. Under certain circumstances the police can ask people for id but I don't think they do ticket you for not having it or refusing to show it. I can't answer your question about how much the fine may be without knowing what you are speicifically charged with. I would fight this if it were me.
The above is for informational purposes only and not meant as legal advice.
Some states require that you identify yourself to an officer; others like my state of CA only punish false statements. It would be important for an attorney like Mr. Robinson to know what statute precisely you are accused of violating. He is the NY expert; CA is my domain.