The A 7♯5 chord and everything around it — the notes and how they are built, the shape on piano and guitar, the sound, and the keys it belongs to.
A7♯5 is A, C#, E#, G — the 1, 3, #5 and b7 above the root A.
Root notes are red. There is no standard open shape for this chord — any group of these notes on the neck sounds the chord.
Every position of the chord tones on the ukulele neck — any group that sounds only A, C#, E#, G plays the chord.
A7♯5 is a colour chord — it is not diatonic to a plain major or minor key, which is what gives it its character. It shows up as a borrowed chord, an altered dominant, or a passing sound.
Work out the chords of a whole key with the Scale & Chord Finder, name a chord from its notes with the Chord Identifier, or browse every chord tool. The theory behind how chords are built is in the free Cloud Atelier music guides.