Cool button.
On the inner ring of letters, I can just make out some of the letters for “JONES” and below that some of the letters for “CORK HILL DUBLIN” reading the opposite way. I would be sure the maker is William Jones of 2 Cork Hill in Dublin, Ireland although there is also an Edward Jones with the same address (and possibly a father-son connection). Known dates of operation are between 1815-1823 (and possibly wider). Obviously, the button can’t be Victorian (ie not after 1838) and in any case the Cork Hill premises were taken over in the 1830s by Hugh Foley.
William Jones is known to have advertised himself as “Button-Maker to His Majesty" and “The King's Button Maker". That means he had a Royal Warrant for production of military or official buttons, not that he actually made buttons for The King’s personal use. He also made livery buttons and that’s what yours is.
Helpfully, we have the full armorial, not just the crest: a chalice or goblet on a shield, crested with some kind of foliage, but I couldn’t find an exact match in Fairburn. That reference work only covers Great Britain and Ireland though and this might have connections to the Snyder / Sneyder / Snider / Schneider / Schnide family which has it’s roots in Germany, with strong connections to emigrants to America during the 18th Century (notably Philadelphia). They used this armorial:
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