How to get input from fingerprint scanner and save it
In technical terms, Android OS stores Fingerprints in TEE (stands for Trusted Execution Environment), TEE is separate and isolated area in phone's hardware or software depending on the way device is manufactured. TEE will never let us in even if device is rooted. Check this for more details about Trusty OS
If your requirement is to get fingerprint signature (which is a critical practice from user's privacy point of view) you'll have to buy a 3rd party fingerprint scanner and integrate with your app.
You can't get fingerprint template or image from android Fingerprint API. Fingerprint data are stored in a secure place by android system and are not accessible.
But you can ask the system to authenticate the user.
Here sample code
The doc, in section Fingerprint Authentication
Although you can't get the fingerprint data from Android's Fingerprint API, you can get it using an external fingerprint scanner which often comes with its own SDK, just check with the manufacturer.