I wouldn't stress about the service of the three day notice. This is just the beginning of a long process. Eviction doesn't happen in couple of weeks. Your main focus should be to show up for the scheduled hearings, coherently explain your position to the judge (a lawyer would be a big help) and think how, or if, you can bring your rent up to date. I assume that's the reason the landlord wants to evict you?
Dear I do not owe maintenance:
Perhaps I might provide an answer.
You obtained your court date (August 20, 2012) when you "answered" the petition in the office of the Housing Court Clerk. Your Answer should state all defenses you rely on to make the court to decide to dismiss the petition.
Defenses based on defective service must be stated in your answer and must be presented in a factual manner that actually controverts the affidavit of the process server.
Your "facts" if stated in your Answer, that you were not in NYC when the process server claimed to serve you in person with the rent demand (the three day notice) and that the notice of petition and petition was "served" on a cooperative employee (the doorman) are real defenses and could result in a dismissal, but only if you stated those defenses in your answer.
Although a defense based upon bad service of the rent demand is not a defense based on a claim of a lack of personal jurisdiction (as would be the ground for dismissal for the improper service of the notice of petition and petition) your answer should have provided some detail regarding your proof that the process server lied about the service of the rent demand.
Technically, the court does not have jurisdiction in a nonpayment summary proceeding when there is no prior demand for the payment of the rent.
Your answer should have stated your defense on the "merits" of the case; that is that no maintenance is owed and the claim in the case is for undocumented late fees and undocumented legal fees. Generally, a nonpayment proceeding should be about a claim for unpaid rent (maintenance in a cooperative) and usually alleged "late fees" and "legal fees" alone should not support a nonpayment proceeding petition.
A good place for you to measure the quality your filed answer in respect of the defenses you presented against a "model" answer is at:
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.