After Sprint and T-Mobile, Verizon has now started rolling out the November 2019 security patch to the Galaxy Note 10, Note 10+ and Note 10+ 5G. It also includes the security patch for the fingerprint recognition.
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The software version of this update is N970USQS2ASJ8, N975USQS2ASJ8, and N976VVRS2ASJ8 for the Galaxy Note 10, Note 10+, and Note 10+ 5G respectively.
Samsung recently rolled out a similar software update for the international unlocked Galaxy Note 10 devices.
If you want to check for the update manually, just head into the Settings > Software update > Download and install.
According to the Fingerprint Recognition Update:
If you’ve used a screen cover, such as a silicone cover with a textured surface on the inside, your device may contain incorrect fingerprint information that may cause recognition issues.
All users should install this fingerprint update. If you’ve registered or scanned your fingerprint with a screen cover on your phone, remove all of your fingerprints and register them again without using a screen cover. Scan your fingerprint in its entirety, including all corners. If you have used a Samsung approved or a factory-applied screen protector you will not need to re-register your fingerprints.