In a large bowl, combine the mashed potatoes, diced ham, shredded cheddar cheese, garlic powder, sliced chives, and 1/2 cup flour. Stir thoroughly until all ingredients are evenly distributed and the mixture holds together.

Lightly flour your hands to prevent sticking, then divide the potato mixture into 16 equal portions. Shape each portion into a small flat disk about half an inch thick.

Heat the vegetable or canola oil in a heavy-bottomed skillet over medium heat. To check if the oil is ready, sprinkle a few drops of water into the pan; if it sizzles immediately, the oil is hot enough for frying.

Carefully add the croquettes to the hot oil in batches, making sure not to overcrowd the pan. Fry each side for about 4 minutes until golden brown and crispy. Flip once during cooking for even browning.

Transfer the fried croquettes to a plate lined with paper towels to absorb excess oil. Let them cool for about 5 minutes before serving.