Did you have a look at the SecSign ID two-factor authentication ? The plugins allow not only for fingerprint logins (as well as FaceID) but add a 2048 bit cryptographic authentication to your login. That way you have a more convenient login and a more secure one as well!
The plugins are ready to be integrated in the cloud in a matter of minutes, without any additional registrations.
Contact me if you need more information, for example about on-premise setups.

To integrate fingerprint authentication with JIRA, the only way I can find is to set up a separate authentication server that manages access from clients using fingerprint readers.

Logon is handled by that server and I guess it logs you into JIRA automatically via web service or something. How they connect I don't understand so well at the moment.

In English, the only company I can find offering such a server is DigitalPersona: www.digitalpersona.com and you can use Microsoft fingerprint readers with that. Seems to cost apx. $1300 for the online server version including 25 user licences.

In Japan, there are some companies offering a similar server/hardware but it seems limited to Japan only, or at least Japanese language customers only.
NTT: http://www.nttcom.co.jp/e-ubf/products/unit.html
Hitachi: http://www.hitachi-hec.co.jp/product/virsecur/shimonni/shimon01.htm

It would be great if JIRA could be upgraded to include fingerprint authentication, to save people setting up a separate server.