How to get the last modification date of a file in a git repo?

The correct way to do this is to use git log as follows.

git log -1 --pretty="format:%ci" /path/to/repo/anyfile.any

-1 restricts it to the very last time the file changed

%ci is just one of the date formats you can choose from others here at https://git-scm.com/docs/pretty-formats