Every fingering that fits a hand
3311
moderate
331x
easy
3566
hard
xab8
easy
What is true of it
A♯sus4 is A♯, D♯ and E♯ — 1, 4 and 5 counted from A♯.
These are also the notes of D♯sus2/A♯ and E♭sus2/A♯. Which name is right depends on what is underneath and what came before — the notes alone do not decide.
The easiest of the 4 fingerings below is 3311: 4 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.
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♯sus4/D♯
x311
A♯sus4/E♯
x566
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.