Green’s Dictionary of Slang

1. a white man’s black or coloured mistress.

1774		E. Long Hist. of Jamaica II 328: Europeans [...] are too easily led aside to give a loose to every kind of sensual delight: on this account some black or yellow quasheba is sought for.
1793		J.B. Moreton West India Customs and Manners 106: When pepperpot and wine his blood alarms, / He takes a quashiba unto his arms, / The melting object pleas’d, then takes her hoe / And works and sings ’till night – ‘Tajo, tajo!’.
[1873		C. Rampini Letters from Jamaica 88: The old African names [...] Quashiba, slender].

2. a mistress in a non-sexual sense, i.e. of a house.

1799		‘Buddy Quow’ in Lalla & D’Costa Lang. in Exile (1990) 111: Gor Mighty da nah Buf / See how Quasheba do me.
1822		S.A. Mathews ‘Dialogue between Uncoo Cudjoe & Buddy Quow’ in Willshire Squeeze 80: You no yerry say Sissy Quasheba hab benuy.
1827		Hamel, Obeah Man II 87: Quashiba! mistress! are you dead?
1828		Marly; Planter’s Life in Jamaica 292: Miss Pindar’s Quasheba, and Miss Goodly’s Clementina, were ladies of honour to Queen Luna.

3. (W.I.) a foolish, uncultivated woman.

1808		J. Stewart Account of Jamaica 160: To use an expression in common use here, many of them [i.e. creole women] (who have not had the advantage of a judicious education, and introduction into polite company) exhibit much of the Quashiba.
1943		cited in Cassidy & LePage Dict. Jam. Eng. (1980).