On Ubuntu/Debian distros, you can easily change the timezone by running the command :
sudo dpkg-reconfigure tzdata
You will be prompt with a list of timezones that you can select from.

You can change it, which os droplet do you have?

You have to login using ssh:

ubuntu:

$ sudo unlink /etc/localtime 
$ sudo ln -s /usr/share/zoneinfo/Indian/<Zone-Of-Your-Choice> /etc/localtime

this will show you all available time zones for Indian

$ ls -al /usr/share/zoneinfo/Indian/