my $basepath = "c:\\foo\\bar";
my $dir = $basepath."\\".$gene."_".$geneid;
mkdir($dir, 0755) or die "Failed creating $dir\n";

chdir($dir);
#what file are you writing?  That is so ambiguous.  Let us pretend $string is your file contents and I will make up a filename becuase you weren't specific about that either.

my $file = "baz.txt";

open(OUT, ">>$file") or die "Cannot open $file for writing\n";
print OUT $string;
close(OUT);