How can I update my iPhone XR to iOS 15.1?

Update it from a computer or through the Software Update function in Settings. If you encounter an issue other than the one listed below, describe it.

Apple no longer signs 15.1; it's not possible to update to that exact version.

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Your iPhone XR can update to iOS 18.7 at the latest. Since iOS 15.1 is no longer signed, you won't have the option of updating to that. "Jump updating" is best performed updating via your computer.