I have an iOS application which supports iOS 6. And I have customers who use this old iOS version (on iPod touch 4). But now I would like to add a framework with iOS 7 as a minimal supported version. Is it possible to release one application in App Store with multiple supported iOS verions with this framework for modern devices and without this framework for old devices?
Not if you're still updating the version that supports iOS 6.
For new updates, if the apps have the same bundle ID, they're only one app as far as the App Store and iOS are concerned. You could do two builds but one would replace the other one in the App Store. You would have to have two separate apps. If it helps, you could set up app groups so that these apps could share data. That might make it easier for people to upgrade from one to the other.
If you're not still updating the version that supports iOS 6, people using iOS 6 will still be able to download that old version even if you release new versions that require more recent versions of iOS.