All Govt colleges in Tamilnadu are governed by Anna University through TANCET. GATE scores are taken and GATE qualified candidates do not have to write TANCET but they can apply for TANCA. I cannot say there will be no fees. A minimum amount always is charged. However GATE qualified candidates can apply for the AICTE scholarships - I think Rs 8000 is the amount and this is dispersed directly through AICTE.

The GATE qualifying scores are mentioned in the brochure check here https://admissions.annauniv.edu/tan17/pdf/TANCA_information.pdf

For the colleges list check this - https://admissions.annauniv.edu/tan17/pdf/TANCA_BOOK_Final_Copy_2017.pdf