How to make an entity that when hurt another entity/player poisons them

Use procedures and source/target entity with entity type check for this. 

Then apply potion using procedure block for this.

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another way of doing that is by adding this to the entity code:

// POISON CODE
		 public boolean attackEntityAsMob(Entity entityIn) {
      		if (super.attackEntityAsMob(entityIn)) {
         		if (entityIn instanceof LivingEntity) {
            		int i = 0;
            			if (this.world.getDifficulty() == Difficulty.NORMAL) {
               				i = 7;
            			} else if (this.world.getDifficulty() == Difficulty.HARD) {
               				i = 15;
           				}

            		if (i > 0) {
               	((LivingEntity)entityIn).addPotionEffect(new EffectInstance(Effects.POISON, i * 20, 0));
            	}
         }

         return true;
      } else {
         return false;
      }
   }
// POISON CODE END

i = duration of poison (in RL seconds)