After configuring multiple business hours (under Admin > Business hours) for the various timezones you are supporting, assign each business hour to groups (under Admin > 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 that all these configurations are available on the Estate and Forest plans.