Hanila,
To set IST for your site, set it to Asia/Kolkata in Site admin > Location > Default timezone.
Asia/Kolkata is the IANA standard reference city for IST: each time zone in each country has one reference city to represent that time zone, and for India that is Kolkata. Use that no matter where you are in IST. All the time zone names starting with "Indian/" , eg. India/Antananarivo, refer to time zone locations in the Indian Ocean.
If you allow users to also change their in timezone instead of forcing the time zone to be the same for everyone (https://docs.moodle.org/39/en/Location), then all times will show up in the user time zone instead of the site timezone, if a user has changed it.
All times and dates in Moodle, such as Quiz due times, are stored internally in a standard absolute format. When a page loads, Moodle converts this absolute time into the proper time zone set for that user, either the site default timezone or the time zone set by the user in their profile (if different from the site timezone). For example, if a teacher in IST sets a quiz to be due at 17:00, and a student has set their time zone to Asia/Kathmandu, the student will see it due at 17:15 their time, which is the same time. A student in Diego Garcia with a time zone set to Indian/Chagos will see the due time at 17:30. However, these are the same moment and it means that the quiz is due for all three of these students at the same moment.
To set IST for your site, set it to Asia/Kolkata in Site admin > Location > Default timezone.
Asia/Kolkata is the IANA standard reference city for IST: each time zone in each country has one reference city to represent that time zone, and for India that is Kolkata. Use that no matter where you are in IST. All the time zone names starting with "Indian/" , eg. India/Antananarivo, refer to time zone locations in the Indian Ocean.
If you allow users to also change their in timezone instead of forcing the time zone to be the same for everyone (https://docs.moodle.org/39/en/Location), then all times will show up in the user time zone instead of the site timezone, if a user has changed it.
All times and dates in Moodle, such as Quiz due times, are stored internally in a standard absolute format. When a page loads, Moodle converts this absolute time into the proper time zone set for that user, either the site default timezone or the time zone set by the user in their profile (if different from the site timezone). For example, if a teacher in IST sets a quiz to be due at 17:00, and a student has set their time zone to Asia/Kathmandu, the student will see it due at 17:15 their time, which is the same time. A student in Diego Garcia with a time zone set to Indian/Chagos will see the due time at 17:30. However, these are the same moment and it means that the quiz is due for all three of these students at the same moment.