After configuring multiple business hours (under Admin > Team > Business hours) for the various timezones you are supporting, assign each business hour to groups (under Admin > Team > Groups). For example, if you have two groups: Support - India, Support - USA, configure two business hours for each of these regions and assign it to the corresponding groups.

You can use the Round-Robin feature for automatic assignment of tickets in the groups.

Note: These configurations are available on the Pro and Enterprise plans (previously Estate and Forest plans.)