Green’s Dictionary of Slang

to not care at all.

1815		D. Humphreys Yankey in England 70: I don’t care a cent for you.
1818		A.N. Royall Letters from Alabama 4 Jan. 124: ‘Poh, poh,’ said the planter. ‘I don’t care a cent for the girls.’.
1843		T. Haliburton Sam Slick in England II 139: Do you think them fellers that keep up such an everlastin’ gab about representation, care one cent about the extension of franchise?
1865		G.A. Sala My Diary in America II 133: I don’t care two cents about seeing the President of the United States.
1875		Auckland Eve. Star (Supp.) 30 Oct. 6/3: Let them [...] howl and carry on, for you don’t care a cent.
1878		F.H. Hart Sazerac Lying Club 188: I don’t care a cent if he did.
1884		(con. c.1840) ‘Mark Twain’ Huckleberry Finn (2001) 81: Steamboat captains is always rich [...] and they don’t care a cent what a thing costs.
1918		A.N. Depew Gunner Depew 205: The Germans did not give a dime a dozen whether we heard them or not.
1918		‘Sapper’ Human Touch 13: I don’t give a ten cent. piece whether a man’s a Catholic or a sun worshipper.
1920		Marvel 24 July 8: Well, I don’t care a cent whether you blame him or not.
1933		R. Chandler ‘Blackmailers Don’t Shoot’ in Red Wind (1946) 115: You don’t care a thin dime about Landrey, now he’s dead.
1938		D. Runyon ‘For a Pal’ in Runyon on Broadway (1954) 573: Blind Benny does not care two cents about the cap business.
1972		D. Jenkins Semi-Tough 121: Personally I wouldn’t give you two cents for him.