Every fingering that fits a hand
323x
easy · no 5
3231
moderate · no 5
3535
moderate · barre
xaaa
moderate · barre · no 5
3235
hard · no 5
What is true of it
A♯6 is A♯, C𝄪, E♯ and F𝄪 — 1, 3, 5 and 6 counted from A♯.
C𝄪 and F𝄪 are double sharps, and they have to be: every letter from A♯ upwards is used once, so the 3 cannot be written any other way.
These are also the notes of Gm7/A♯. Which name is right depends on what is underneath and what came before — the notes alone do not decide.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 5 fingerings below is 323x: 3 fingers, held at the 2nd 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.
2 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.
1 string stays silent.
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
A♯6/C𝄪
x231
A♯6/E♯
aaaa
A♯6/F𝄪
0211
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.