1. the least value or merit; nothing or anything at all: It's not worth a tinker's damn.
2. care or give a tinker's damn , to have or feel little or no concern; be unaffected or unmoved: I don't care a tinker's damn for their opinions.
Also, tinker's dam .
[ 1830-40; from tinkers' alleged habit of cursing frequently (hence weakening the force of a curse) ]