>> You may log onto the website of the district or the high court within whose jurisdiction, the properties of your deceased Fahter are situated.....................
The fee fixed by the court may be say.............up to 3% of the value of the stamp duty on the property...............
A local lawyer/ deed writer may also in a position to inform you the specific amounts.
They can also guide you that depending on the value of the estate of the deceased, the matter shall go to the type of court (pecuniary jurisdiction) which can conduct cases for that value.
All details might be available on the website of the district or the high court e.g;
https://delhihighcourt.nic.in/writereaddata/upload/CourtRules/CourtRuleFile_5V1ZJF9S.PDF
While in case of legal heir certificate from Tehsildar the time for issuance may be say............15 days and fee may be less.
>> In your case the issue is only the delay and limitation expressed by Tehsildar.
There is no issue like as per report of the Revenue Inspector it is difficult/not possible to establish the legal heir.
You may go thru :
Madras High Court
M.N. Arumugam vs The Tahsildar on 9 March, 2011
https://www.indiankanoon.org/doc/1476659/
If you feel that certificate from Tehsildar is possible and option is better you may explore the merits.
A local lawyer can guide you further.
You may pursue the option that is deemed suitable at your end.