Yes, you can apply RTI to obtain Copies of your Answer Sheets from Tamil Nadu Public Service Commission (TNPSC).
TNPSC was established under an Act of the Madras Legislature in 1929 and was the first Provincial Public Service Commission in India. It operates under Articles 315 to 323 of Part XIV of the Constitution of India. The working of TNPSC is also regulated by Tamil Nadu Public Service Commission Regulation, 1954 and the TNPSC Rules of Procedure. TNPSC is a Department of the Govt. of Tamil Nadu responsible for governing the Recruitment of Personnel into the State's Public Service. Hence, TNPSC is a "Public Authority" as per Section 2 (h) of the RTI Act 2005.
You can file RTI to obtain Certified Copies of your Answer / OMR Sheets under Section 2 (j) of the RTI Act from TNPSC by addressing the same to the designated "Public Information Officer (PIO)" through Registered Post and by paying the prescribed fee. You should attach a Copy of your Admit Card and mention your Roll No., Registration No., Name of the Exam clearly in the Application.
To know more about the procedure to file RTI Application for Exam Paper, please refer https://onlinerti.com/how-to-file-rti-online-for-exam
To know more about the procedure to file RTI Applications in the State of Tamil Nadu, please refer https://onlinerti.com/how-to-file-rti-online-for-tamilnadu