Add mashed potatoes, ham, cheese, garlic powder, chives and ½ cup flour to a large bowl. Stir together with a wooden spoon until combined.
Lightly flour your hands and divide the potato mixture into 16 small flat disks, about half an inch thick. TIP - use a cookie scoop to get perfectly even portions.
Heat oil in a heavy bottomed skillet (I recommend cast iron if you have it). TIP - you can test if the oil is hot enough by sprinkling a few drops of water in. If they sizzle, it’s ready.
Fry the croquettes in batches, flipping once, about 4 minutes per side until golden. Transfer to a paper towel lined plate. TIP - don’t crowd the pan; leave space between each croquette so they crisp all around.
Cool 5 minutes before serving.
Add a little more flour if they aren’t holding together well enough. Judge the amount of oil based on your pan. They shouldn’t be completely immersed in oil, but there should be enough to crisp all around.