One should ALWAYS sign a written retainer when dealing with an attorney.
If you have a fee dispute, you should contact the Fee Dispute Program in your area.
When you retain an attorney you should always sign a written retainer.
Check with a lawyer in your locale to discuss more of the details.
Good luck to you.
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The bar associations and the attorney licensing authorities generally have fee dispute mediation programs. I would google them up in NY and call them right away to get the dispute into mediation.
I find it hard to believe an attorney would start working on a case like this without a written, signed fee agreement. You have an absolute right to a copy of your file so you might start with a written demand, sent certified mail, return receipt requested, requesting a copy of your complete file, including fee agreement,all documents of whatever nature signed by you, and all other file documents, within 10 days of the law office's receipt of the request.