This plant has been growing in my garden (south India) for a while. Would like to know its name so that I can take better care of it. Thanks!

This plant has been growing in my garden (south India) for a while. Would like to know its name so that I can take better care of it. Thanks!

This is definitely some kind of Cacti plant.
I would say it's from the Schlumbergera group.
It's quite easy to multiply by just cutting one of the healthy leaves and putting it in light humus in another pot.