My iPhone 13 keeps restarting on its own

Hello~ Try a forced restart…

Force restart iPhone - Apple Support

Then check your battery health…Go to Settings > Battery, then tap Battery Health & Charging. What’s the %? If 80% or below get your battery replaced by Apple…

Genius Bar Reservation and Apple Support Options - Apple

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~Katana-San~

"My iPhone 13 keeps restarting on its own: My iphone 13 is restarting on its own, first time happened i thought ut was an update but turns out it’s the phone doing it on it’s own"

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Fixing a Boot Loop:

Your iPhone is reportedly stuck in a Boot Loop. This typically occurs when you go abuut installing an update, and it stalled while in the process. Use my User Tip: How to Fix an iPhone in a Boot Loop - User Tip