The standard grips this chord is usually shown with.
AmMaj7 is A, C, E and G#, a minor major seventh. The shape this page opens on is written x02110, lowest string first.

Also written AmM7, Am(maj7), A-Δ7 or AminMaj7. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 7 common shapes for AmMaj7 on the guitar, and 34 derived voicings in 4 families.
The common shapes, written lowest string first: x02110, x32254, xx7554, 576555, xx7998, x-12-10-9-9-x, x-12-14-13-13-12.
Shell. Root, third and seventh: the guide tones fix the quality, so the fifth is dropped. That is what leaves a string free, so pick a tension to put on top. AmMaj7 has x065xx, x0x11x, 536xxx, 5x65xx, x-12-10-13-x-x, x-12-x-13-13-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. AmMaj7 has x0211x, 4322xx, xx6555, 5765xx, xx7998, x-11-10-9-10-x, x-12-14-13-13-x, xx2214.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. AmMaj7 has 4x221x, x0x110, x3x254, x7x595, 5x655x, 8x799x, x-11-x-9-10-8, 12-x-10-13-10-x.
Open string. An open string left ringing against a fretted grip. Because it costs no finger, it sounds a note the closed shape has none left for -- a tension on top, or a pedal root underneath. Either a familiar grip with open strings added, or a shape so sparse the open strings carry the chord. These belong to their key rather than to a shape, so D, A, G and E have many and Eb a handful. AmMaj7 has 57650x, 5x6500, 43220x, 030254, 000504, 4x0500.
Tensions. A shell of AmMaj7, root, third and seventh, leaves a string free, and the tones that belong over it are the 9 (B), the 11 (D) and the 13 (F#).
The common shapes and the derived voicings come from different places, and both are explained in where the chords and the theory come from.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.