well if you look at fundamentals and basic tonal theory, a minor 3rd is "dissonant", hence the slight sense of displeasure or unhapiness we find in it. but yea, but typical standards i don't think a minor 3rd would be a dissonant interval. the flat 5th, minor 2nd and major 7th are the most dissonant tones.

getting a dissonant chord can be as simple as implimenting these notes or just using diminished (b5) or augmented (+5) intervals are the easiest ways to create dissonance.

cool chords are:

fully diminished (1, b3, b5, b7)
french 6th (1, 3, b5, 7)
minor chord with a major 7th (1, b3, 5, maj7)
dominant 7 #9 (1, 3, 5, 7, #9)

^^^last one is quite dissonant because the #9 is only a half step away from the 3rd of the chord, creating the most dissonance. you might find it displeasurable but it's dissonant nonetheless.

these might be hard to understand if you don't understand how to build chords. i'm basing these numbers off the notes of a major scale. so, a 3 would be the 3rd note of the major scale, etc. after 8 (the octave) we keep on going to build "extended chords" like we see in jazz. so, a 9 is really a 2, an 11 is a 3, etc. just minus 8 from the higher number and viola. it's good to just remember that a 13 means a 6, and so on.