During its nearly four centuries as a Spanish colony Cuba had no real coinage of its own. First Spanish and then mostly Mexican coins were used.
In 1898, the warship U.S.S. Maine—sent to Cuba to observe the Cuban revolt against the Spanish—exploded in Havana Harbor. As a result of the ensuing war, the Spanish lost their Cuban colony, and American currency then became legal tender on the island.
Cuba obtained its (conditional) independence in 1902, and a dozen or so years later, its first national coinage appeared. This copper-nickel 1915 1-centavo is a first-year example of the low-value in the series:
The new coin series numbered some 12 different denominations, but consisted of 13 different coins. (The 1-peso denomination appeared in both silver and gold.) The thirteen members of this first Cuban coin series of 1915: 1-, 2-, 5-, 10-, 20-, and 40-centavos, 1-peso silver and 1-peso gold, and 2-, 4-, 5-, 10- and 20-pesos.
This 1915 1-centavo was coined in Philadelphia, as would subsequent Cuban coinage be, until the success of Castro and his revolution. Beginning about 1962*, Cuban coins were struck at what was once Czechoslovakia’s Kremnica mint, and a little later, also at the Leningrad mint in the old Soviet Union.
*I have encountered discrepancies between sources regarding this date, and haven't yet resolved them.