use grep:

my $r = 44;
my $hash = $self->{'residues'}{$modelCount};
for my $key ( grep { /^\w$r$/ } keys %$hash ) {
    print $key."\n";
}
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Update:Yup, as abigail suggested use each for large hashes so you dont duplicate the memory needed for the keys:

my $r = 44;
my $hash = $self->{'residues'}{$modelCount};
while( my ($key, $value) = each %$hash ) {
    next if $key =~ /^\w$r$/;
    print $key."\n";
}
[download]