Auth/EPP code is used as a protection mechanism to ensure that only the rightful domain owner can control the transfer of the domain registration. It is one of the essential security measures against unauthorized transfers.
Some hosting companies may tell you that this is the only way to verify the domain for using hosting with them, but please be aware that it should be requested only if domain registration is being transferred to them, and there are alternative methods of verification like change of nameservers, etc.
If the Auth/EPP code is provided to your hosting provider, your domain may be completely transferred to them.
In case you do wish to completely transfer your domain registration out of NityGity to the system of your hosting provider, you can check this article for details on how that can be done.