Certain abilities let you push targets, normally 20 feet.
Shove pushes targets 20 feet
Warlocks Eldrich's blast as well.
What the rules on pushing target off a ledge?
The relevant rules are:
How to Play, Basic Rules, page 3
Shoving a Creature, Basic Rules, page 74
Falling, Basic Rules, page 65
Saving Throws, Basic Rules, page 62
My ruling is:
"Pushing a creature off a ledge," on its own, is the goal of a fictional action that lacks an approach. An acceptable approach to achieving that goal might include a spell that forces the target back or some other pushing attack such as shoving a creature. The approach is adjudicated by the DM and, if the outcome of that action is found to be uncertain, the DM calls for the appropriate check e.g. a contest of Strength (Athletics) versus the target's Strength (Athletics) or Dexterity (Acrobatics) in the case of a physical shove. The resolution of the check and its proximity to the ledge in the fiction determines whether or not the target is pushed off the ledge. In most cases, no additional mechanics need apply. There may be some corner cases where the target may get to make a saving throw to avoid falling because the fictional circumstances provide an additional shot at avoiding the fall.
But you or your DM may make a different ruling based on this or other criteria.
I agree with both Iserith & OoftaMeg while there doesn't need additional mechanic to see if someone is pushed over or off a ledge, I do think that creature or person should have a chance to catch themselves like if someone fell trying to climb.
However, personally if it was a minion creature I wouldn't give it a save. Whatever you decide it should be equal between NPCs and players so if the players do it and there's no save then no save for them either.
However, you or your DM may make a different ruling based on this or other criteria.
Just don't roll a 1 when you attempt to push them off the ledge, else you might end up meeting your future partner.
I allow the target to spend it's reaction on a choice of str (athletics) or dex (acrobatics) to catch the ledge with a DC based on the ledge, and is treated as prone.
I'm pretty sure that Chris Perkins gives the victim a strength or dexterity check to catch a ledge, etc. I think that is a holdover from 4e rules too.
It seems to work fine.
To me it matters how far away the ledge is. If you ability lets you push them 15 ft, and the ledge is 10-15' away, I give them some sort of save. If the ledge is closer than that, no save or a very hard save.
Even if they make the save, there is a negative consequence, prone or AC penalty or....
In 4e since everything happened on a grid, you knew who was "close enough" (or wasn't) to the ledge to be knocked off. They still got a save if you tried it.
My Dark Sun Druid finished off an encounter all by himself because he had
a "helicopter",
a ranged at-will shove power,
enemies with only melee attacks,
said enemies on a 1-square-wide ledge,
and as long as he needed to get the dice to cooperate.
Once the DM figured out that I had unbeatable tactical advantage, he just gave us the Encounter.