So i know that these formulas get the chords for these scales:

Major Scales
Major Minor Minor Major Major Minor Dimished

Minor Scales
Minor Diminished Major Minor Minor Major Major

so what's the formula for Modes and lets say Exotic Scales (Japanese, Bebop, Pentatonic Minor and Major, Byzantine, etc)? For these scales do I pick any chords that can be created by the notes that are only within the scale? I mean for example like sometimes if you use the numeral system youll get chords with a note that's not in the scale example (B diminshed in the C Major Scale)

Also I know in styles of metal its common to use these chords (1+5 aka power chord and the 1+3 or 1+b3) when can i use these in major/minor scales? If so do they replace any other chords (from the numeral system)?
what. this is a very confusing post.

1st. a B diminished chord IS derived from a C major scale...
2nd. i think you should look to pick scales based on chords, rather than chords based on scales (if that makes sense.) as in, you should have a chord progression that you want to solo/write a melody over, and then you should analyze it and figure what scales you could play over those chords, not the other way around so much.
3. the pentatonic scale is not exotic in the slightest.
chords are created from picking every second note from the root of a scale.

example C D E F G A B C

chord 1 =CEG (M)
2=DFA (m)
3=EGB (m)
4=FAC (M)

hope it helps
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by the B diminshed example I meant that Bdim is made up OF B,D,F,G# and the NOTE G# is NOT IN THE C MAJOR SCALE! >_<

Whoisthisguy I understand that but how would one figure out chords for exotic scales without tediously having to go through the intervals in each key matching notes to see if they match the notes of the scale because as of now that is the only way i see how one could use chords that would fit the sound of exotic scales or one would have to use power chords >_< ?
well that's because it's not really b diminished.

B diminished is just B D F.
B half diminished (or min7b5) is B D F A, and is the chord found in the C major scale.
B fully diminished (the chord you're thinking of) is B D F Ab, and would most often be found in C minor, due to the raised leading tone.

i suggest checking up on your theory (maybe reading the big ol' theory sticky that's on here) because that could really help you figure this stuff out.

and the only way to find out what chords can be found from a certain scale, is to go through and construct triads (and eventually more expanded chords if you choose) from each note of the scale. but i think before you try and jump into topics like this, you should try and understand what's going on with the chords progressions and scale patterns in simpler concepts like major and minor keys, which is what most songs are, and are the real fundamental building blocks of all of this.
usually, (though i'm no expert on the topic, and i don't have any examples of what you're looking at/listening to) the more exotic scale ideas you hear/see aren't from any real far out chord progressions, but are more just adding color to more simpler major or minor progressions.