How to get rid of annoying offers to update iOS?
Unfortunately, without jailbroken this can not be done. We recommend to update iOS to the latest version, all supported devices on iOS 10 work no worse than on the previous version of the system.
Is that you have to use an iPhone or iPad with a rarity iOS 6. In this case, you can jailbreak and not only turn off the notification with a proposal to update, but also delete the firmware file that has long been downloaded to the device. Otherwise, there are no objective reasons for not updating.