Min/Maj 7 Chords
The min/maj7 chord is a minor triad (1st, b3rd, 5th) with a major 7th added on top. So it is kind of the opposite of a dominant 7, which is a major triad with a minor 7th on top.
Here's some examples of how we could finger it on the guitar:
The min/maj 7th chord can be used as a root chord in minor harmonies and is derived from the harmonic minor scale (which contains the sharp 7th).
See Harmonizing the Minor Scale for more information.