Not exactly. It seems I voiced it inconsistently, though.

A G# minor 7th in this example would be G#, B, D#, F# - but since the F is natural, it doesn't fit in this definition. It would be an altered minor 7th (up to you how you name it depending on voicing)

You could call it some kind of G#6 chord; Ab min 6 would be A♭ C♭ E♭ F, which is enharmonically equivalent.

The actual error here is calling it G#, as opposed to F. I'm not sure why I made that error is given that the precise voicing is clearly written (in my own picture I created, no less!) as F, B, D#, G# - a half-diminished 7.

I suspect its because I was reading about the many interpretations of the chord by scholars, each of which make decisions based on which of the four notes is the root. I read some simply argued the G# was a very slow passing tone, rather than part of the chord and... well, it goes on.

The point is, the chord is interesting! I'll make an edit with this in mind either way, cheers!