Place the chicken breasts in the bottom of a slow cooker.
In a medium bowl, mix together the zesty BBQ sauce, chicken broth, apple cider vinegar, smoked paprika, garlic powder, onion powder, and black pepper until well combined.
Pour the BBQ sauce mixture over the chicken breasts in the slow cooker.
Cover and cook on low for 4 hours, or until the chicken is tender and easily shredded with a fork.
Remove the chicken breasts from the slow cooker and shred them using two forks.
Return the shredded chicken to the slow cooker and stir to coat with the sauce.
To assemble the sliders, place a generous scoop of the shredded BBQ chicken on the bottom half of each slider bun.
Top each with a slice of dill pickle and a sprinkle of shredded cheddar cheese.
Place the top half of the slider bun on each sandwich and serve immediately.