Hello,
You can appear next year for the exam with a new registration.
Candidates who wants to get better choice of college/branch are eligible to apply for second phase counselling but number of counselling rounds may increase in case of vacant seats.
So there is no possibility that you can go for 3rd round as the special round is also closed now.
Click on the link for details
https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/articles/ts-eamcet-counselling/amp&ved=2ahUKEwjx7tD1r5T1AhVoSmwGHXwbDTQQFnoECAwQAQ&usg=AOvVaw3qb5ZmUlcCTwc2htZjbUEQ
Thanks
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