not care a hang (about something)
To not care in the slightest (about something or someone); to attach no importance to someone or something. I don't care a hang about making money, I just want to do something with my life that makes life better for others. I haven't cared a hang for the show ever since they killed off my favorite character. Do whatever you want, I don't care a hang.
not care (or give) a hang
not care at all. informal Hang here is a late 19th-century euphemism for damn .