An app that pops up on top of any other app on iOS

Question

例如，即使要运行另一个应用程序，内置闹钟应用程序也要在响铃时启动（它不仅显示通知）。

Answer 1

At WWDC 14 Apple showed off the Extensibility feature. You shouldn't be able to do it on iOS 7 but in the future(iOS 8) you can use the extensibility in third party applications.

For more information read the mashable blog : http://mashable.com/2014/06/02/apple-ios-extensibility/

Answer 2

Not on an iOS device :D.

Only 1 app can be presented on the screen at one time.

Maybe in iOS 8 with split screen feature perhaps?

Although that isn't quite exactly what you want.