1. You are required to take registration for your Chennai Branch Office (SEZ)
GST law is silent about separate registration of SEZ unit located in SEZ. Accordingly, SEZ unit will have to take registration under GST for either principal place of business or additional place of business.
2. IGST ( though supply to SEZ is zero rated supply , it will not be treated as export for you as you will be considered distinct person for that matter )
Section 7(5) of the IGST Act, 2017 provides that supply of goods and/or services, when the supplier is located in India and the place of supply is outside India and to or by a SEZ developer or a SEZ unit shall be deemed to be a supply of goods and/or services in the course of inter-State trade or commerce.
As per section 2(5) of IGST law, ‘export of goods’ means taking goods out of India to a place outside India. Therefore, to be called as export of goods, goods should cross the territory of India.
As per section 2(6) IGST law ‘export of services’ is defined to means
the supply of any service when
the supplier of service and recipient of service are not merely establishments of a distinct person in accordance with section 25(4) of the CGST Act, 2017.
3. Services from SEZ will be as per normal GST charges (depends on place of supply and suppliers location )
Supply of goods and/or services by the SEZ units or Developers from SEZ to DTA would be covered under the normal course of supply.