Every fingering that fits a hand
2140
easy · no 5
2444
moderate
2144
hard · no 5
214x
easy · no 5
x99b
moderate · barre · no 5
What is true of it
Amaj7 is A, C♯, E and G♯ — 1, 3, 5 and 7 counted from A.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 5 fingerings below is 2140: 3 fingers, held at the 1st fret.
None of them uses an open string, so this chord moves up the neck unchanged — the same shape 1 fret higher is the chord a semitone above.
1 of the 5 need a barre.
It leaves out the 5. 4 strings cannot carry 4 notes, and the 5 is the one this chord can lose without changing what it is.
Where its notes are on the neck
The brass dots are A, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
Amaj7/C♯
6440
Amaj7/E
999b
Amaj7/G♯
1100
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.