Java Edition:Trident with Incompatible Enchantments
The Riptide enchantment cannot be applied to the same item with Channeling or Loyalty currently. From 18w07a-18w11a (1.13 snapshots), this wasn't the case, they could be combined. In 18w14a (1.13 snapshot) they made them incompatible. However, the trident was not obtainable in survival until 18w11a.
Obtaining Trident
Trident + Trident
A trident with Riptide CAN'T be combined with a trident with channelling/Loyalty.
Trident + Book
In an anvil, a trident with some of the enchantments can be combined with an enchanted book with some of the other enchantments.
Enchanting Table
Using an enchanting table directly, it is possible to get up to all 4 trident exclusive enchantments with various levels by enchanting it directly.
Obtaining Book
An enchanted book containing the incompatible trident enchantments is also possible.
Anvil Combination
Enchanting Table
Generated Structure Loot
Fishing
Trading
Enchantment Effects
From 18w07a through 18w11a, all enchantments on a Trident will work as intended. You will be propelled forward in water and rain with Riptide, while launching the trident further than yourself, returning to you with Loyalty, and Channeling will strike lightning on a mob if there is a thunderstorm. Unfortunately, in later versions the trident with both or all three of these enchantments has no special effects and will act identical to a trident that has only Riptide. Channeling won't strike lightning when running into a mob and Loyalty doesn't occur because the trident is never thrown away from the player.