not give a fig
(not) give a fig
slang To be concerned about someone or something. Typically used in the negative to convey the opposite. I don't give a fig about making money, I just want to do something with my life that makes life better for others. I haven't given a fig for the show ever since they killed off my favorite character. Do whatever you want, I don't give a fig.
not give (or care) a fignot have the slightest concern about.
Fig was formerly used in a variety of expressions to signify something regarded as valueless or contemptible.