You can use glob to find all the file names matching that format. I'll use POSIX::strftime to generarte the glob pattern with today's date. Given the file names, I'll slurp each and count the number of matches to some $re.

use POSIX 'strftime';
my $date = strftime '%Y%m%d', localtime;

my $re = qr/whatever/;
my $count = 0;

for (glob "/path/to/*$date*") {
    local $/;  # to slurp
    open my $fh, '<', $_ or warn $! and next;
    my $content = <$fh>;
    close $fh;
    $count += () = $content =~ /$re/g;
}

print $count,$/;
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The odd construction where $count is incremented is a common perl idiom for getting a list of matches and counting them. It places the bind-and-match in list context, then the resulting list is evaluated in numeric scalar context. Be cautious about capturing in $re. Multiple captures will produce extra elements in the list.