Legal Question in Immigration Law in New York

Although it is a little difficult to understand your situation, generally, if a petition or application is denied for failure to respond to an RFE that one claims to have responded to, the respondent can file a Motion to Reopen within 30 days of the denial, with evidence proving that the RFE was responded to in a timely manner.

However, if you were originally petitioned by your mother, then there should not have been a condition put on your residency in the first place.

If your mother is a U.S. citizen & you are under 21, then, yes, she could petition you again for a "greencard", if your CR status (?) is terminated.

It is difficult to understand what you are saying in your question, however it looks like you responded to the RFE in time but just forgot to annotate it with your Alien Number or Receipt Number, which it sounds like you still you are lucky, because apparently the USCIS sent you a letter acknowledging receipt at first, but then denying receipt later on. This isn't really a question of law but rather a question of administration and clerical. The best mechanisms to deal with this might be either by making an InfoPASS appointment to go in and physically speak to someone at USCIS, or to prepare and file an AILA Liaison Inquiry in order to get someone to correct the misunderstandings inside the system. Please call my law office at 2129688600 to discuss. Thanks, RDM