After Sprint, T-Mobile has now started rolling out the November 2019 security patch to the Galaxy Note 10 and Note 10+. It also includes the security patch for the fingerprint recognition.
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The software version of this update is N970USQS2ASJ8 and N975USQS2ASJ8 for the Galaxy Note 10 and Note 10+ respectively. The size of this update is more than 200MB.
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.