Green’s Dictionary of Slang

a farthing.

1911		J.W. Horsley Memoirs of a ‘Sky Pilot’ 254: Other [words] were new to me, such as [...] ‘dadla’ or ‘fadger’ for a farthing.
1926		Derby Dly Teleg. 7 Apr. 3/3: Every coin has some slang name [...] tush [...] quidlet [...] fadger.
1943		R. Llewellyn None But the Lonely Heart 159: What did he have when he kicked it? [...] not a fadger in the world.