The Fingerprint Authentication is offered from Android 6.0+. It is not supported for lower versions.
Refer this example for Fingerprint Authentication (for above android 6.0)
https://github.com/googlesamples/android-FingerprintDialog
I also found a easy tutorial that might help you in this regard.
https://dzone.com/articles/android-fingerprint-authentication-tutorial
For previous android version each company such as Samsung, Motorola, HTC created its own API and SDK to access to fingerprint sensor.
For instance Samsung provide a SDK http://developer.samsung.com/galaxy#pass
Pass SDK allows you to use fingerprint recognition features in your application. With Pass SDK, you can provide reinforced security, since you can identify whether the current user actually is the authentic owner of the device.