Every fingering that fits a hand
1312
moderate · barre
x878
easy · no 5
What is true of it
G♯m6 is G♯, B, D♯ and E♯ — 1, b3, 5 and 6 counted from G♯.
These are also the notes of Fm7♭5/G♯. Which name is right depends on what is underneath and what came before — the notes alone do not decide.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 2 fingerings below is 1312: 3 fingers, one of them barring the 1st fret, 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.
1 of the 2 need a barre.
Where its notes are on the neck
The brass dots are G♯, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
G♯m6/B
4546
G♯m6/D♯
8878
G♯m6/E♯
abbb
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.