Relevant portion of 'Description of Service' at S. No. 7 of Notification no. 12/2017 CT reads as follows:
Services provided by the Central Government, State Government, Union territory or local authority to a business entity with an aggregate turnover of up to twenty lakh rupees (ten lakh rupees in case of a special category state) in the preceding financial year ........."
Hence, this exemption is available even for a registered person with an aggregate turnover of up to twenty lakh rupees (ten lakh rupees in case of a special category state) in the preceding financial year.
Furthermore, this exemption-entry is unconditional. What this really means is that tax-rate of such services is NIL. And tax-payer was NOT having option NOT to claim such exemption while deciding to pay taxes under RCM.
As subject amount related to FY 20-21, even normal time limit of 2 years to claim refund is not yet lapsed.
Hence and without going into larger question about applicability of time-restrictions to claim refund, I suggest to file refund on above grounds.
All above are strictly personal views of mine and same should not be treated as professional advice / suggestion.