Restrict to certain iOS target devices for App Store submission
Unfortunately not at the moment, there is a list of options available for you to restrict the user from purchasing the app but nothing for restricting due to the cores
List:
http://developer.apple.com/library/ios/#documentation/general/Reference/InfoPlistKeyReference/Articles/iPhoneOSKeys.html
Restricting IOS app in app store to certain devices
You cannot distribute through app store and target some specific device.
If you publish on the app store then the app becomes visible to all.
If you would like to make some kind of restriction than make a login screen through which you open up the rest of the app, and give the credentials to your specific customer.
Is there a way to not support my app from iPad or selected iPhone versions?
For restricting your app to only iPhones devices after the app was already published on App Store you should reupload new version of your app to App Store by simply just changing target devices to iPhone only(with different Bundle Identifier of course).
About restricting your app to stop supporting older devices(4,5,5S) you should change your iOS version compatibility. For example iOS 13 is supported on iPhone 6s and newer devices so user won't be able to use it on older devices. Apple should handle this on their own.
There are some alternatives to restrict your app to specific devices with Required device capabilities key which you can find in your Info.plist file. But I don't think apple will accept this, if this features are not actually used in your app.
Here is the documentation about UIRequiredDeviceCapabilities in case you need it.
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