Great Britain used to mint fractions of farthings for British colonies to emulate local denominations.
A farthing was 1/4 of a British penny or 1/960 of a British pound
At the time these were minted a British pound was worth around United States $5 making the farthing worth about 1/2 of a cent.
We have here coins worth 1/4 of a US cent and 1/6 of a US cent.
It is amazing that there were things which could bought for such small amounts then.
Here are four fractional farthings:

Great Britain fractional farthing - 1/2 farthing 1844
Queen Victoria facing left
Crown, HALF FARTHING
Copper, 18 mm, 2.4 gm

Great Britain fractional farthing - 1/3 farthing 1868
Queen Victoria facing left
Crown and wreath, ONE THIRD FARTHING
Bronze, 15 mm, 0.9 gm

Great Britain fractional farthing - 1/3 farthing 1902
King Edward VII facing right
Crown and wreath, ONE THIRD FARTHING
Bronze, 15 mm, 0.9 gm

Great Britain fractional farthing - 1/3 farthing 1913
King George V facing left
Crown and wreath, ONE THIRD FARTHING
Bronze, 15 mm, 0.9 gm
Here are all four fractional farthings with a United States dime:

The 1/2 farthings were minted for Ceylon (now Sri Lanka) to emulate the local duit or (British) India pie.
A pie was 1/12 anna or 1/192 India rupee; a rupee was worth about 48 US cents then.
The 1/3 farthings were minted for Malta to emulate the local grano.
There were also 1/4 farthings for the big spenders.
