In NY how can a judgemet be entered against me if I was not even living in the state at the time of service?

In New York (and other states as well) there is no requirement of any kind that someone be a resident in order to have a judgment entered against them. Residency isn't even a prerequisite for commencing an action against an individual.

The jurisdictional limit of a court is only related to the actions of the individual: otherwise someone could order a product from a company in one state and have it delivered to their home in another, and then simply refuse to pay with relative impunity, knowing that the company would have to sue in the state of residence, rather than where the sale occurred.

Just because you failed to appear in court does not mean a judgment cannot be rendered against you. If you are referring to small claims court, then someone with a grievance against you filed a case. The court sent a certified letter to you, at your last known NY address, advising you of the suit, the court date, and time you should appear. If you didn't get it....too bad; they did all they have to do. You didn't show up to defend yourself or dispute the claim; the judge was forced to rule in their favor, assuming they had the slightest legal claim to their suit. Apparently, they did. You lost.

Many rules of law regarding publication requirements for a defendant who isn't able to be found; contact the court that placed the judgement.

Happens in divorce and custody all the time.

Because you still could have responded to the summons explaining that you lived out of state, hardship, etc. You could still contact and hire a lawyer to represent you without the need for you to be present. Many things you could have done. But didn't.

If it wasn't important enough for you to exercise your right to defend your position, then you defaulted. Judgement against you. Pay up.

need more details please - sounds like you received some kind of service (living there or not)