Green’s Dictionary of Slang

a symbol of cuckoldry, thus tip (someone) turnips, to cuckold.

1818		‘A. Burton’ Adventures of Johnny Newcome III 169: Snoring in the arms of Joey, Calliope lay drunk as Chloe! [...] She opened her eyes without confusion, And utter’d with a maudlin squall, ‘I’ve given you turnips, Jack— that’s all!’ [Ibid.] 258: Turnips, the Cyprian symbol of Cuckledom.
1840		Flash Mirror 19: He has tipt N. Nickem turnips, and gone to live at the Duck and Salt Box.
1849		Sam Sly 17 Feb. 2/3: If you continue to eat so many pennyworths of plum-pudding you will become as corpulent that the lovely Julia will give you turnips, so look out.
1873		G.W. Hunt ‘Bom! Bom! Bom!’ 🎵 Her Bobby love, with his carroty hair, / She gave him ‘turnips’ then and there. / She scorned his bull’s eye and his staff, / Prefered her soldier’s love by half.