What is true of it
A♯dim7 is A♯, C♯, E and G — 1, b3, b5 and bb7 counted from A♯.
The easiest of the 1 fingering below is 3434: 3 fingers, one of them barring the 3rd fret, 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.
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♯dim7/C♯
6767
A♯dim7/E
9a9a
A♯dim7/G
0101
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.