I can’t update my software

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IOS update? Your iPad mini 3 isn't compatible with an IOS version higher than IOS 12.

See the article(s) below which show device compatibility for each IOS version. 

iOS 16 compatible devices

IOS 15 and iPadOS 15 Compatible Devices.  *

iOS 14 and iPadOS 14 Compatible Devices.  *

iOS 13 and iPadOS are compatible with these devices - Apple Support.  *