Blend all ingredients in a high-powered blender, on high, for 20 seconds. Strain the mixture through a fine-mesh strainer into a glass jar or measuring cup, using a spoon to push the juice through the strainer to remove the pulp. Discard the pulp.
Add about 1/4-1/3 of a cup of the juice to a glass with ice or a coupe glass. Top off with sparkling water, non-alcoholic ginger beer, or ginger ale. Garnish with cinnamon sticks or sliced ginger.
Notes
Apple cider ice cubes - Freeze the juice in an ice cube tray and/or store any remaining juice in a glass bottle or mason jar in your fridge for up to 5 days. Then top with ginger beer or ginger ale for a flavored drink!
Turmeric can be omitted from the recipe, if desired. If you do this, you also don't need to add the fresh pepper.
I recommend Topo Chico for the most carbonation for sparkling water, and Fever Tree or Regatta light for ginger beer.