Take two, with builtins only. Note that with readdir, it doesn't keep the whole path, so you have to add it back manually:

use warnings;
use strict;

my $dir = 'test';

opendir my $dh, $dir or die $!;

while (readdir $dh){
    if (/tpsm_.*/ && -f "$dir/$_"){
        print "$dir/$_ is a file\n";
    }
}
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update: or use glob as Corion said :)