According to the New York Bar Association, to be appointed Judge in New York, one has to be a U.S. Citizen, a Naturalized Citizen, or a Permanent Resident Alien.
Born in Columbia, do we have any evidence that Merchan went through a formal Naturalization process, or is Trump at the mercy of a resident alien?????
Who do you mean by "we"? I wouldn't expect him or anyone else to send you personally a certified copy of his naturalization papers.
Considering how long he's been on the bench, and the fact that neither Trump nor any other party or attorney that has ever appeared before him has raised this as an issue, it's pretty safe to assume he meets the basic legal requirements for the job.
But if that isn't enough for you, you can always prepare and submit a NY freedom of information act request for those records.
Good luck!