Every fingering that fits a hand
3055
easy · no 5
3253
hard · no 5
What is true of it
A♯maj9 is A♯, C𝄪, E♯, G𝄪 and B♯ — 1, 3, 5, 7 and 9 counted from A♯.
C𝄪 and G𝄪 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.
On an instrument that cannot reach all 5, the 5 and 1 go first, in that order.
The easiest of the 2 fingerings below is 3055: 3 fingers, held at the 3rd 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.
It leaves out the 5. 4 strings cannot carry 5 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
A♯maj9/C𝄪
7988
A♯maj9/E♯
acac
A♯maj9/G𝄪
2213
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.