Dear Ahmad, 

Yes you can register and apply for deemed university in second or before mop-up round as well, since the registration opens before every counselling round. The payment option will be made available to you at the time of registration (if you haven't already paid). 

The reset initialization option at registration page is for candidates to enable them to re-register with new quota choices (AIQ/Deemed/etc.). It allows them to reset the previously filled quota choice and fill the particulars again and then proceed for registration. However, this facility is provided only once. You will be able to avail it in mop-up round registration too. 

Hope it clears. 

All the best!