While it is true that this topic is from over a decade ago, it is one of the first things that turns up if one searches for "New York Catechism", meaning people searching will come across this topic, so it felt prudent to post here for reference.
For recap: There is a quote people sometimes share that is attributed to a work called the "New York Catechism". It reads thusly:
"The Pope takes the place of Jesus Christ on earth …by divine right the Pope has supreme and full power in faith, in morals over each and every pastor and his flock. He is the true vicar, the head of the entire church, the father and teacher of all Christians. He is the infallible ruler, the founder of dogmas, the author of and the judge of councils; the universal ruler of truth, the arbiter of the world, the supreme judge of heaven and earth, the judge of all, being judged by no one, God himself on earth."
The original source of this quote is a work called Roman Catholicism (1962) by Loraine Boettner. He gives the above quote and attributes it to the aforementioned "New York Catechism." No information about this catechism is given, nor a page number. It is often claimed by Catholics that the work simply does not exist.
The original poster here apparently was told that, but then made this topic to offer a claim that it does exist, linking to a (no longer available) discussion on the Catholic Answers Forum. It appears that in said discussion, it was suggested the work being cited as "The Catholic Catechism" by Pietro Gasparri, which was printed in New York. However, it was apparently also noticed that the quote was not actually found in the work.
When this topic occurred, there was no way for anyone to look it up for themselves unless they found a physical copy, so all of this discussion was based on secondhand information. But since then, copies of Pietro Gasparri's work are available for reading online. You may view it here (I have set it to link directly to the relevant page, page 98):
Gasparri The Catholic Catechism 1932 : Gasparri, Pietro, 1852–1934 : Free Download, Borrow, and Streaming : Internet Archive
Or, if one would prefer a version that only shows two pages at a time (the above one shows four), you can view it here:
The Catholic Catechism 1932 Gasparri : Free Download, Borrow, and Streaming : Internet Archive
The pages linked above are the closest thing one finds in the catechism to what is quoted from the "New York Catechism". However, what we actually see in the document is this:
"The Roman Pontiff is called the visible head of the Church and the Vicar of Christ on earth because, since a visible society needs a visible head, Jesus Christ made Peter, and each successor of his, to the end of the world, the visible head and the viceregent of His own power... By divine right the Roman Pontiff has over the Church a primacy not only of honour but of jurisdiction, and this both in things concerning faiths and morals and in discipline and government... The Roman Pontiff has supreme, full, ordinary, and immediate power both over each and every Church, and over each and every Pastor and his flock... The lawful successors of the Apostles are, by divine institution, the Bishops; they are set over particular churches by the Roman Pontiff, and govern them by their own proper power under his authority."
The book is written in question-and-answer format so all the ellipses I used above are doing is taking out the questions. Some parts are a bit similar to the quote offered, but even those are paraphrases, and some parts of the the quote attributed to the "New York Catechism" do not appear at all in the above, including the most controversial part (where it refers to the pope as "the arbiter of the world, the supreme judge of heaven and earth, the judge of all, being judged by no one, God Himself on earth.")
So, if this is the "New York Catechism", then the quote offered from it is very inaccurate. If this is not the "New York Catechism", then we return to the fact we've simply been unable to find it (aside from the early 19th century Episcopalian catechism sometimes referred to as such, which is clearly not what is in view, and does not seem to have the quote either as far as I can tell), and it is difficult to take the quote seriously if it cannot be verified.
So I suppose this post up until this point didn't add any new information, but did add confirmation of the information given.
As long as I'm discussing this topic, I suppose I might as well add one more thing, namely this:
https://www.google.com/books/edition/Sadliers_Catholic_Directory_Almanac_and/b-DQAAAAMAAJ?hl=en&gbpv=1&dq="new+york+catechism"&pg=RA5-PP23&printsec=frontcover
This is a Catholic almanac from 1883, and it includes an advertisement for what it calls the "Small New York Catechism", the full title of which is "The Catechism; or, A Short Abridgment of the Christian Doctrine. Newly Revised. For the use of the Catholic Church in the United States. To which is added a Prayer before and after Catechism." I seem to recall someone somewhere else (cannot remember where) saying that this might have been the work in question. While I cannot find a copy of the work to be absolutely sure, I do not think it is what is in view. This is most likely simply a New York printing of the catechisms you can find here that have a similar title (specifically containing "A Short Abridgment of the Christian Dotrine, Newly Revised"):
A Catechism or short abridgment of Christian doctrine [microform] : newyly revised for the use of the Catholic Church : Catholic Church. Diocese of Quebec : Free Download, Borrow, and Streaming : Internet Archive
A Short Abridgment Of The Christian Doctrine; Newly Revised And Augmented, For The Use Of The Catholic Church In The Diocese Of Boston ; published with the approbation of B. Fenwick. : Catholic Church. Archdiocese of Boston (Mass.) : Free Download, Borrow, and Streaming : Internet Archive
(their prefaces are slightly different but once the catechism itself starts, they seem identical)
If the "Small New York Catechism" is simply that catechism printed in New York, it would disqualify it because those do not contain the quote (a search indicates the pope is only mentioned once, and not in conjunction with the quote). Additionally, if this was the catechism, it was printed prior to 1883--it is hard for me to believe that given the hostility to Catholicism that was present at the time, that no Protestant critic of the Catholic Church apparently took notice of this quote until nearly a century later. In any event, if this work improbably does contain the quote, the onus is on the person advancing the quote as accurate to demonstrate it.
Anyway, like I said because information is now easily available online that was not available at the time of this topic, and the fact that this topic turns up as one of the top hits if one searches for "New York Catechism", I felt it would be good to share this extra information that one can use to confirm for themselves that it is not found in Gasparri's catechism, because otherwise this topic was entirely secondhand reports on what Gasparri's catechism said.