You cannot file IT returns without Aadhar number.
You should either have Aadhar number or Aadhar enrollment number.
Supreme court has extended date for linking to beneficial schemes. Filing it return is not a scheme.
Further IT department has been asking for Aadhar linking from a very long time.
Those who do not have Aadhar number will not be able to file return unless government makes any changes on its website or extends date for filing of IT returns. Chances of any extension are very low, lets wait and watch.