Every fingering that fits a hand
3545
moderate
324x
easy · no 5
3241
hard · no 5
3245
hard · no 5
xaab
moderate · barre · no 5
What is true of it
A♯7 is A♯, C𝄪, E♯ and G♯ — 1, 3, 5 and b7 counted from A♯.
C𝄪 is a double sharp, and it has 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 4, the 5 goes first, in that order.
The easiest of the 5 fingerings below is 3545: 4 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.
1 of the 5 need a barre.
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♯7/C𝄪
7868
A♯7/E♯
aaab
A♯7/G♯
1211
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.