... with filenames that are based on those numbers.

If the derivation of filename from ID is predictable, it might be more efficient to create a hash of filenames from the IDs then use grep to select appropriate files from your @files array rather than keep looping over files and IDs.

use strict;
use warnings;

my @IDs   = qw{ pj7023 ge4872 dr90324 jc824 };
my @files = qw{
   XYZ_dr90324.txt
   XYZ_at728.txt
   XYZ_jc824.txt
   XYZ_uf72082.txt
   XYZ_tc43.txt
   XYZ_pj7023.txt
   XYZ_yj82195.txt
   XYZ_fw607.txt
   };

my %IDnames =
   map { my $key = q{XYZ_} . $_ . q{.txt}; $key => 1 }
   @IDs;

my @selectedFiles =
   grep exists $IDnames{ $_ },
   @files;

print qq{$_\n} for @selectedFiles;
[download]

The output.

XYZ_dr90324.txt
XYZ_jc824.txt
XYZ_pj7023.txt
[download]

It might be that the filename can't be confidently derived from the ID and this method will not work but I thought I'd post the idea just in case.