How can i make a living entity apply a custom effect by hitting the player?

Make a procedure with the global trigger 'before entity is hurt.' In that procedure, use an if bracket to check that the event/target entity, (the one being hurt), is a player, and the source entity, (the one attacking), is the desired type of mob. (You can do this using the 'is entity subtype of ' function in the logic tab.) Then, inside the if bracket, use the 'apply potion effect' function to apply your custom effect to the event/target entity.

If you make a procedure, you can find the 'apply potion effect' function in the 'entity management' tab. It's a blue code-block that asks for an entity, a duration, and a potion effect, and applies the effect to the entity you provide it with.

If you're really new to making procedures, it may be worth looking into some of NorthWestTree's tutorials on youtube to get a better idea of how they work.