You can apply for HSEE - 2020 only by online mode through the official website of HSEE - 2020 (hsee.iitm.ac.in)
After applying you have to pay the examination fee as applicable through Net Banking / Credit Card / Debit Card / Indian Bank e-challan.The e-challan will be generated during the process of application. The examination fee for SC, ST and PwD candidates is Rs.1200/-. The examination fee for All other Candidates is Rs. 2400/-. Additionally, service charges of the Bank will be Rs.40/-.
for detailed application procedure follow this link to the official website of hsee :-
Hope this helps,
All the best!