require 'newPackage.pl';  #exporting the package namespace

What require does is not exporting something, but opening your script, and running it again - which is why you get output twice.

I'd write that as

use strict;
use warnings;

{
    #creating a package
    package newPackage;
    sub subroutine1 {
        print "*This is a new package called from within the file*\n";
    }
}



print keys(%newPackage::),"\n";
print "\n\n";
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Also you should load packages with use, and exporting is done with Exporter.