Every fingering that fits a hand
x666
moderate · barre · no 5
babx
easy · no 5
bab9
hard · no 5
What is true of it
F♯6 is F♯, A♯, C♯ and D♯ — 1, 3, 5 and 6 counted from F♯.
These are also the notes of D♯m7/F♯ and E♭m7/F♯. 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 3 fingerings below is x666: one finger, one of them barring the 6th fret, held at the 6th 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 3 need a barre.
It leaves out the 5. 4 strings cannot carry 4 notes, and the 5 is the one this chord can lose without changing what it is.
1 string stays silent.
Where its notes are on the neck
The brass dots are F♯, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
F♯6/A♯
3324
F♯6/C♯
6666
F♯6/D♯
x321
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.