Rub the pork shoulder with smoked paprika, salt, and pepper. Place it in a slow cooker and pour ½ cup of the BBQ sauce over the top.
Cook on low for 6 to 8 hours until the pork shreds easily with two forks. Shred the meat directly in the slow cooker and stir in the remaining ¼ cup of BBQ sauce.
In a mixing bowl, combine the shredded cabbage, grated carrot, mayonnaise, apple cider vinegar, sugar, salt, and pepper. Stir until the slaw is evenly coated.
Split the slider buns and lightly toast them in a skillet over medium heat if desired. Spoon pulled pork onto the bottom halves and add a generous spoonful of slaw on top. Close with the bun tops and serve right away.