The CAGED system is basically a generalised theory and not usually specific to Minors. I have included them into this area just so you can get an idea of how minors are associated to majors. If you wanted to you could also make a CAGED system using Sevenths, Diminished and Augmented's and so on. I would suggest mastering the CAGED system in majors and then learn how to change every C Major, A Major, G Major, E Major and D Major chord into minors, 7th, major 7th an so on.
C Minor Shaped Bar Chord
This is not a common shape on the guitar, it twists the finger around to get into position and I rarely see it being used in songs. So why do it? The simple fact is that it exists! so don't ignore it. Try to get use to all the common extensions, Minor, 7th, Major 7th, Minor 7th & Suspended, all around the CAGED system.