Fake ledge jumping is an advanced technique in SSB64 that can only be performed by Samus and Jigglypuff, due to their floatiness and ability to teleport.
It allows the player to "slide" in the air, being unaffected by gravity for a few frames and thus being able to return to the stage without the need for a second jump. Like drop cancelling, it can only be done on a ledge that ends diagonally upwards.
To execute this technique, the player must dash towards the ledge and hit the opposite direction on the stick at most 3 frames before going off the ledge.
Video
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