The foreign bank branches in Korea are for providing their services to their corporate customers in Korea. Most of them don't offer the retail banking services in Korea and a few branches offer limited retail banking services.
Also, the foreign bank branches in Korea don't share the customer and account information with the branches in their home country. Hence, even if you have an account in your home country, they can't provide the banking services with it in Korea.
If you need to withdraw money from your bank account in your home country, you need to issue an ATM card from the bank in your home country and use it at a Global ATM in a Korean bank branch.
For more information about banking services, contact the bank branch.
State Bank of India is an indian government-owned bank and they have a branch in Seoul. Currently, they're providing corporate banking and private remittance service for Indians living in Korea.