The easiest way is to use readdir together with stat and sort.

Something like this:

use 5.020;

my $dir = '\\\\server\\share\\my\\path';

opendir my $dh, $dir
    or die "Can't opendir '$dir': $!";
my @files = map { "$dir\\$_" }   # convert filenames to absolute filen
+ames with UNC path
            grep { !/^\.\.?\z/ } # ignore "." and ".."
            readdir( $dh );

my %last_modified = map { $_ => -M $_ } # cache the last modified time
                    @files;

@files = sort { $last_modified{ $a } <=> $last_modified{ $b } } @files
+;

say $files[0];
[download]

Update: Ignore . and .. entries, spotted by Marshall