How do I limit an iOS app only to 4 inch screen devices?

Nope.

Because iOS 7 supports devices with 3.5" screens, you can't use the only-support-iOS-x technique.

Also, there isn't a setting in Xcode or a key for requiredDeviceCapabilities which allows you to make the app 4-inch only.

As you can see in below screenshot which is taken from Apple's official website, iPhone 4 and iPhone 4s are the ones with 3.5 inch screen and they do support iOS 7.

So you cannot constrain the app resolution support for 4 inch screen only by even using iOS 7.

Also as per the below forum there is no way we can just put application on app store that only supports 4 inch screen iPhone.

iPhone app for 4-inch screen only?

Let me know if you need more help.