Green’s Dictionary of Slang

a threepenny bit coin.

1907		Hull Dly Mail 19 July 3/7: For the ‘nimble threepenny dodger’ everyone will have the chance of winning one of the [...] prizes.
1934		Yorks. Post 7 May 9/3: These ‘artful dodgers’ accumulate [...] the treasurer disclosed he had over 500 threepenny pieces.
1940		Hull Dly Mail 23 Mar. 4/4: The coin must have been a greater nuisance than the oft-maligned ‘threepenny dodger’.
1948		Hull Dly Mail 13 Sept. 3/4: Surmising on ‘threepenny joey’ [...] Mr Meldrum’s grandmother still refers to them as ‘threepenny dodgers’.
1993		(con. 1920s) W. Woodruff Road to Nab End (2003) 55: ‘Tha’re a grand lad,’ they said giving me a tanner (6d.) or a dodger (3d.).