Every fingering that fits a hand
3044
easy · no 5
3143
hard · no 5
What is true of it
A♯m9 is A♯, C♯, E♯, G♯ and B♯ — 1, b3, 5, b7 and 9 counted from A♯.
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 3044: 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♯m9/C♯
6044
A♯m9/E♯
ac9b
A♯m9/G♯
1014
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.