Is there any way to install apps incompatible with Android 4.1.2 (Jelly Bean)
The Android Market pulls the OS version directly from the system.  As far as I'm aware there's no way to fake this other than building a custom ROM that fakes it, or possibly some sort of code injection.

As ce4's comment says, you'll need to obtain the app from a different device running a supported OS or through some other means (a different app store for example).