The variable $dir is not interpolated when you use single quotes, try changing them to doubles: "$dir/Hsapiens_fasta_folder"

The idea of File::chdir is to not use chdir() and use $CWD instead:

#!/usr/bin/perl
use strict;
use File::chdir;
my $dir = '/data1/sgb';
$CWD = "$dir/Hsapiens_fasta_folder";
my @files=<*.fa>;
$CWD = "$dir/targetp-1.1";
foreach my $file( @files) {
    print "$file\n";
    print "$CWD\n";
}
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