a cent, as representative of triviality: His promise isn't worth a red cent.
Origin of red cent
An Americanism dating back to 1830–40
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019
(used with a negative) informal, mainly US a cent considered as a trivial amount of money (esp in the phrases not have a red cent, not worth a red cent, etc)
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
Online Etymology Dictionary, © 2010 Douglas Harper
see under not worth a dime.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.