Handle of my faucet is calcined
The photo appears to be of a very old, possibly nickel-plated brass fixture with the plating worn off and a significant copper-based corrosion process ongoing.
I doubt that you'll find any quick fix here as you'll either need to replace it entirely or completely disassemble it, remove all corrosion from it, re-plate it as appropriate, and replace all of its worn parts before it will work as new again.
I'm sure you can find some articles online about this process. Cleaning off the corrosion is likely to be easy enough. I'd start with a product such as CLR or similar that is sold where you live. That, plus some steel wool, should yield a cleaned-up surface. Plating takes special equipment and while it can be done yourself, if you want nice results you should find a local shop that does this.