Have you tried deleting old info and setting up again, this article may help
https://www.imore.com/troubleshooting-touch-id
It covers Touch ID on Mac and iDevices, so look for the relevant section.
The only other thought is to Restore the device as new and see if that resolves, if not a trip to the Apple Store might be required.
Restore your iPhone, iPad, or iPod touch from a backup - Apple Support