Squirreled away in my closet are some (supposedly) high-quality photocopies of several documents including the Constitution. That comma is in the original too. It hasn’t been added as far as I can tell. If I knew how to do it, I’d scan that section and post it here but I have to plead techno-ignorance as my defense.
Copied verbatim from the US Constitution ‘transcript’ located at the U S National Archives website:
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
I have the Constitution hanging on the wall in my living room and there is no comma in that position.
It reads:
No person except a natural-born citizen, or a citizen of the United States at the time of the adoption of this Constitution, shall be eligible to the office of president....
There is no comma after "States" and before "at" in the copy on my wall.