Green’s Dictionary of Slang

a squinting or injured eye, or a person who has one.

1849		Sam Sly 13 Jan. 2/2: Why, you had much better pay your debts and look after your beautiful boss-eye.
1866		J. Greenwood Little Ragamuffin 213: She [...] was called [...] by an appellation suggested by her visual deprivation, ‘Boss-eye.’.
1881		Harry Hunter ‘Put me some Jam Roll by, Jenny’ [ballad] Come where the waves roll high, Jenny, / Come with your old boss-eye.
1897		W.S. Maugham Liza of Lambeth (1966) 45: ‘Puddin’ fice!’ she cried. ‘Kite fice!’ ‘Boss eye!’.
1912		P.C. Wren Dew & Mildew 164: [T]he obiter dicta of his hero brother, Bossy (who had a slight cast in one eye) .
1926		Breton & Bevir Adventures of Mrs. May 22: ’Awkins ’ad a boss eye.
1980		Barltrop & Wolveridge Muvver Tongue 91: Bad eyesight and deafness are mildly ridiculed: ‘boss-eye’, ‘cock-eyed’.