Perhaps something like this will do what you require UNTESTED:

my %hash = (
    aw1 => 10,
    qs2 => 20,
    dd3 => 30,
    de4 => 10,
    hg5 => 30,
    dfd6 => 20,
    gf4 => 20,
    hgh5 => 30,
    hgy3 => 10,
    );

{   # exchange number values for filehandles

    open my $FILE1, '>', '10.txt' or die "Cannot open '10.txt' $!";
    open my $FILE2, '>', '20.txt' or die "Cannot open '20.txt' $!";
    open my $FILE3, '>', '30.txt' or die "Cannot open '30.txt' $!";

    for my $val ( values %hash ) {
        $val = $FILE1 if $val == 10;
        $val = $FILE2 if $val == 20;
        $val = $FILE3 if $val == 30;
        }
    }

local @ARGV = glob 'Data/*.fa';

my $name;
while ( my $line = <> ) {
    if ( $line =~ /^>(.+)/ ) {
        $name = $1;
        }
    print { $hash{ $name } } $_ if exists $hash{ $name };
    }
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