I'd recommend you look at safe exam browser - it doesn't do biometrics but looks at other issues around secure exams. You could also implement some form of Quiz access rule to do this like these plugins:
https://moodle.org/plugins/browse.php?list=category&id=41
You might also find Vinnie Monaco's work interesting (using keystroke dynamics to recognise a user.)
https://docs.moodle.org/dev/BioAuth_Plugin
http://www.vmonaco.com/
There is also a plugin from edu-labs that might be worth looking at (which isn't listed in the official plugins db so hasn't been through a code review by the plugins team)