Are there any cheat codes (certain combinations of buttons, etc.) on the PS4 edition of Skyrim? I was hoping there might be a code that gives me a jump boost or reduced fall damage, as I'm currently stuck on the side of a mountain with no way up or down.
No, there are no cheat codes. On Windows, you can use the console, but that isn't possible for the PS4.
As fja3omega mentioned in a comment, your best bet is probably to use fast travel to move somewhere else. You could also try to run/jump sideways along the rocks and get to somewhere more convenient.
If you happen to know the Become Ethereal shout, just use that and then jump off the cliff. You'll survive the fall no matter how far it is.