B# Major is not a real key signature. It's what is called an "imaginary key signature" - one that can be figured out theoretically, but isn't practical, and therefore not used.
However, you can derive a scale from any note by going up the progression of T, T, ST, T, T, T, ST - so, the notes of B# major would be:
B#, Cx, Dx, E#, Fx, Gx, Ax, B# (where "#" is a sharp and "x" is a double-sharp)
If you are talking about just the chord of B# major then the same thing applies. It is an "imaginary chord" whose note would be: B#, Dx, Fx.
G major, D major, E major, B major, F sharp major, F sharp minor, A sharp major, etc.
B sharp, C double-sharp, D double-sharp, E sharp, F double-sharp, G double-sharp, A double-sharp, B sharp.
B-natural, D-sharp, F-sharp
C major: no sharps, no flats F major: no sharps, B flat Bb (B flat) major: no sharps, B and E flat Eb major: no sharps; B, E, and A flat Ab major: no sharps; B, E, A, and D flat Db major: no sharps; B, E, A, D, and G flat Gb major/F# (F sharp) major: no sharps; B, E, A, D, G, and C flat / F, C, G, D, A, and E sharp; no flats B major: F, C, G, D, and A sharp; no flats E major: F, C, G, and D sharp; no flats A major: F, C, and G sharp; no flats D major: F and C sharp, no flats G major: F sharp, no flats
C# major, E major, A major, B major, and C# minor.
15 different key signatures exist. (no sharps or flats) = C major F sharp= G major F C sharp = D major F C G sharp = A major F C G D sharp = E major F C G D A sharp = B major F C G D A E sharp = F # major F C G D A E B sharp = C# major B E A D G C F flat = C flat major B E A D G C flat = G flat major B E A D G flat = D flat major B E A D flat = A flat major B E A flat =E flat major B E flat =B flat major B flat = F major
G major, D major, E major, B major, F sharp major, F sharp minor, A sharp major, etc.
B sharp, C double-sharp, D double-sharp, E sharp, F double-sharp, G double-sharp, A double-sharp, B sharp.
B-natural, D-sharp, F-sharp
C major: no sharps, no flats F major: no sharps, B flat Bb (B flat) major: no sharps, B and E flat Eb major: no sharps; B, E, and A flat Ab major: no sharps; B, E, A, and D flat Db major: no sharps; B, E, A, D, and G flat Gb major/F# (F sharp) major: no sharps; B, E, A, D, G, and C flat / F, C, G, D, A, and E sharp; no flats B major: F, C, G, D, and A sharp; no flats E major: F, C, G, and D sharp; no flats A major: F, C, and G sharp; no flats D major: F and C sharp, no flats G major: F sharp, no flats
Yes, B sharp does exist in music theory. It is the enharmonic equivalent of C natural, meaning that they are the same pitch but spelled differently.
C# Major
B Major and G sharp minor. The sharps are F, C, G, D, and A sharp, in that order.
C# major, E major, A major, B major, and C# minor.
B major, or G sharp minor. The sharps are F, C, G, D and A. F#, C#, G#, D#, A#
That would be either A major or F# minor.
A, B, C sharp, D, E, F sharp, G sharp, A