Dear Vidhya,
Your question is very vague. There are a number of labor laws applicable in Tamil Nadu, both Central and State laws. A mere mention of the number of a form will not be a sufficient point of reference unless the Act or Rules under which it is prescribed or additional relevant particulars like the nature or type of the establishment or the class of employees in such establishment have been mentioned in your query.
From a very limited guess, I presume the Form III you mentioned must be the approved list of festival holidays under the Tamil Nadu Industrial Establishments (National and Festival Holidays) Act, 1958.