A

It's an 11th position chord because of the position of the first finger but it's based around the A on the 14th fret.

The 3 and the 6 sound cool together and with the 5 in the bass it is starting to outline an A chord, proceed with caution though.

Could be a good option for a minor chord if you're up this way

The minor chord with the 5 in the bass, taken from the open position Cm chord.

Based on the 2nd position barre chord the b7 note is the open G on top. Note that there is no 3 though so you can't make a tritone and you lose the essence of the 7th chord. An easy shape though and it can still be useful for quick chord changes.

This moveable shape gives a great sounding minor seventh chord, even without the root note.

With the 5 in the bass and the tritone on top this is one of the better options for a 7th chord, a good moveable shape to learn.

This one has the 3 but no root so can sound a little odd, you choose. A common moveable shape though based on the D major in the 3nd position.

For a jazzier sound in your minor chords.