Scales to Play Over G#maj7
Every chord is a subset of several scales: any scale that contains all of a chord's tones fits over it. Pick a chord to see the matching scales from its own root, the major keys the chord belongs to, and full fretboard diagrams for every scale on guitar.
A G#maj7 chord contains the notes G# – C – D# – G. Any scale that includes every one of those 4 tones fits over it — from the root G#, that means G# Major, G# Lydian and G# Mixolydian Bebop. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
G#maj7 is also diatonic to 2 major keys: D# major (relative minor Cm), G# major (relative minor Fm). In a song from one of those keys you can also solo with the key's own major scale or its relative minor pentatonic across the whole progression, not just this chord.