Is there a picture of the Santa Claus three dollar bill?

Answer 1

Pictures of Santa are also on "real" one-dollar bills, as a decorative sticker you can peel off.

(see the related link for an image of an 1854 bill featuring Santa Claus)

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There is no such thing as a genuine modern $3 bill featuring Santa Claus. There are many such novelty items that are privately made and sell for a couple of bucks in toy stores and holiday shops.

But there was one once...

There was, in fact, a legitimate $3 bill with Santa Claus featured on it. This was in a time when individual banks or states issued their own currency, during the 1850's. Some of the banks who issued the bill were: Howard Banking Company of Boston, the Central Bank of Troy, the Pittsfield Bank, White Mountain Bank, St. Nicholas Bank of Manhattan, and the Central Bank of NYC in 1852. And it was legal tender!

The notion that they were fake comes from scams which did put out a lot of fake bills, including $3 ones.

(see related links)