In a case where there is very obvious instance of fraud (e.g. producing fake document in order to get out of an obligation), but it is so obvious that the other party did not rely on it - what causes of action does this party have? fraud upon the court?
A civil action seeking money damages for fraud requires that someone was injured by the fraud. If no one believed that the fraudulent document was real, then no injury would be caused by it and there would be no cause of action for fraud. (There is a more esoteric body of law that governs situations when a person is hurt by fraud because a third party relies upon a fraudulent statement.)
There are potentially other sanctions that could exist for attempting to defraud someone but failing to do so.
For example, some criminal statutes make it a crime to attempt to defraud someone or to forge a document, attorney regulation discipline can be imposed against an attorney who engaged in fraudulent conduct without regard to harm, and many states have laws that criminalize false consumer advertising without proof of reliance.
But, without more context regarding the nature of the fraud, it is impossible to know what is appropriate. You seem to be referring to a fraudulent document presented to a court in New York State, but haven't provided enough context to know if that is indeed what is involved or to understand what you are really asking. This is not a question with a general answer that applies in all circumstances.