I am unable to put a UK visa appointment fees refund request before my appointment date

The sequence of your events is not entirely clear from your query, but you may have a bit of a problem obtaining a refund if you did not withdraw your application, in writing, and cancel the appointment 5 days in advance.

According to VFA Global India

The visa fee will be refundable only if the application is withdrawn in writing prior to the biometric submission, or if the applicant refuses to provide biometrics. User Pay Visa Application Centre fees will be refundable only if the appointment is cancelled 5 days before the scheduled appointment date.

It is also not clear whether you wish a refund of your VFS service fee; see whether this link will allow you to submit a request.

If you wish a refund of your visa fee from UKVI, you would have to do so through Visa4UK:

1. Sign into your Visa4UK account using your email address and password;
2. Select the option ‘View Appointment’ for your application;
3. Select the option ‘Cancel Appointment’;
4. Select ‘Yes’ in the following confirmation dialogue box;
5. Select the option ‘View Payment’ for your application;
6. Scroll down to ‘7. Request Refund’ and select the option ‘Request Refund’;
7. Explain your reason(s) for requesting a refund in the area provided and then select the option ‘Apply for refund’.

Receiving your refund may take up to 28 working days.