Scales to Play Over C#6
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 C#6 chord contains the notes C# – F – G# – A#. Any scale that includes every one of those 4 tones fits over it — from the root C#, that means C# Major, C# Major Pentatonic, C# Rock 'n' Roll, C# Lydian, C# Mixolydian, C# Dorian Bebop, C# Mixolydian Bebop, C# Half Whole Diminished and C# Gypsy Major. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
C#6 is also diatonic to 3 major keys: C# major (relative minor A#m), F# major (relative minor D#m), 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.