Heat a large nonstick skillet over medium-high heat and add the oil. You want the oil to be between 325 and 350 degrees F - you can always test a drop of the batter first to see if it's hot enough. Dip the fish in the batter and coat it completely, then drop it in the skillet to fry. Let each piece of fish fry until the sides appear golden and crispy, about 3 to 4 minutes per side. Gently remove the pieces with a spatula and place them on a paper towel to absorb any liquid. Repeat with all the fish, adding more oil if needed.
To assemble the sandwiches, add a bit of tartar sauce on the bottom of each bun. Top with a piece of fish, then with the slaw. Serve immediately!