How Do I make Specific Existing Mobs Drop Modded Items

You could do this with a loot table. You may have to look up the loot table name for the mob you are affecting, but as long as you get the name right it will change the vanilla loot table.

https://youtu.be/aDAhhLADH_M

1. Create a new procedure.
2. Set the global trigger to "When entity dies".
3. If [event/target entity] is (sub)type: (desired vanilla entity)
   • Spawn gem at [x, y, z].

If you want an existing mob from another mod, you can also do a string comparison for name from the entity registry name