I'm assuming `stat` being "too verbose" means the command outputs a lot of other information too, which it does by default if you don't request specific bits of info from it.
With GNU `stat`:
stat --printf '%y\t%n\
' -- *file*
That would output only the modification timestamp in human-readable format followed by a tab and the filename. This will be done on all filenames that contains the substring `file`. Set the `dotglob` shell option in `bash`, with `shopt -s dotglob`, to also allow hidden filenames to be included.
Use `%Y` in place of `%y` to get the modification timestamps in seconds since Epoch instead.
On BSD systems, use
stat -f '%Sm%t%N' -- *file*
instead (does the same thing). Change `%Sm` to `%Fm` to get seconds since the Epoch.
See the manual for `stat` (`man 1 stat`) on you system for further information.