Green’s Dictionary of Slang

madza n.

also medza, medser, medzer, midzer
[Ital. mezzo, a half]

1. (Ling. Fr./Polari) a half; thus madza beargured, half-drunk, madza round the bull, half a pound of steak.

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[UK]Hotten Dict. of Modern Sl. etc. 61: MADZA, half. [Ibid.] n.p.: MADZA ROUND THE BULL, half a pound of steak.
, , [UK]Hotten Sl. Dict. [as cit. 1859].
[UK]P.H. Emerson Signor Lippo 47: They come at madza nova butchers to inspect and see all is bona.
[UK]P. Baker Fabulosa 294/2: medzer, mazder half.
[UK]R. Milward Man-Eating Typewriter 30: [She[ minnied aimlessly around the city in a medsa-wakey rev.

2. a halfpenny.

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[Aus]Morn. Bulletin (Rockhampton, Qld) 18 July 2/6: A half-penny [...] ‘Madza’ (English) and ‘ mag ‘ or ‘magg’ (Scotch) are synonymous, and mean literally a trifle made; no matter whether begged, borrowed, or stolen.
[Scot]Dundee Eve. Teleg. 19 July 2/4: [A] halfpenny is a ‘brown’ or a ‘madzer (pronounced ‘medzer’), ‘saltee’ [...] ‘mag,’ ‘posh,’ ‘bawbee,’ or ‘rap’.

In compounds

madza caroon (n.) (also medsa-caroon) [caroon n.]

half a crown, 2s 6d (12½p).

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[UK]Hotten Dict. of Modern Sl. etc.
[Aus]Melbourne Punch ‘City Police Court’ 3 Oct. 234/1: The Mayor. – What’s the name of the lug chovey in which you lumbered the prop? Prisoner. – It wasn’t lumbered at all, your honor’s lordship. She sold it for a madza caroon in a lush crib, and got lumpy with the dibbs.
[UK]Sl. Dict.
[UK]Nottingham Eve. Post 9 Oct. 5/5: Romany oprigin [...] also applies to ‘madza caroon,’ meaning half a crown [...] Thus we have ‘madza saltee’.
[UK]P. Baker Fabulosa 294/2: medzer caroon half a crown (money).
[UK]R. Milward Man-Eating Typewriter 121: Felching the trummuses of these detestabnle arroganki gillies [...] for the odd manky medsa-caroon.