Super Jump Punch
The Super Jump Punch is a third jump that Mario, Luigi and Dr. Mario can perform in all three titles. It is executed by pressing B while holding the control stick upwards; thus, it is their up B attack. When performed by either of the "Marios", they jump up diagonally with more vertical range than horizontal; if the attack strikes an enemy during the jump, coins fly out of the enemy, and the foe receives about 10% damage.
Luigi
Luigi's Super Jump Punch only deals 1 point of damage, and has little knockback. However, if the attack's sweet spot hits a character, it becomes a powerful Fire Jump Punch which deals around 25% damage with high knockback. In SSBM, Luigi's attack sends him vertically without any horizontal range, forcing him to rely on his Green Missile for recovery. In Brawl, Luigi turns upside down at the peak of his jump, falling on his head. This allows for more horizontal movement after the move but has more landing lag compared to his Melee Super Jump Punch.
Special Usage
Additionally, in both Brawl and Melee, Dr. Mario and Mario can "aim" their Super Jump Punch straight up vertically by holding the control stick in the opposite direction they are facing during the "spark" of the Super Jump Punch's animation. On a side note, in relevance to the technique and appearance of the attack, some people also call this move the Pay-Day Punch.
Origin
In the original Super Mario Bros. Mario and Luigi could hit blocks from below. Some of the blocks had coins they would release. This is where the coins that are released when this move is performed with Luigi. Also, in the original Super Mario Bros., both Mario and Luigi hit the blocks with their fist. This is the reason they punch like that when they are performing the move.