Every fingering that fits a hand
x102
open · no 5
6877
hard
6474
hard · no 5
6477
hard · no 5
647x
easy · no 5
What is true of it
C♯m7 is C♯, E, G♯ and B — 1, b3, 5 and b7 counted from C♯.
These are also the notes of E6/C♯. 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 5 fingerings below is x102: 2 fingers, held at the 1st fret.
1 of them use open strings, which is what makes a shape quiet to change to.
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 C♯, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
C♯m7/E
9b9b
C♯m7/G♯
1102
C♯m7/B
4444
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.