Scales to Play Over A#dim7
Every chord is a subset of several scales: any scale that contains all of a chord's tones fits over it. Pick a chord to see the matching scales from its own root, the major keys the chord belongs to, and full fretboard diagrams for every scale on guitar.
A A#dim7 chord contains the notes A# – C# – E – G. Any scale that includes every one of those 4 tones fits over it — from the root A#, that means A# Half Whole Diminished, A# Whole Half Diminished and A# Gypsy Major. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
A#dim7 is not diatonic to any major key — it is a chromatic color chord, so treat it as a moment of tension: lean on its chord tones from the scales above, then resolve to the surrounding key when the progression moves on.