Heat 1/4 inch of oil in a 12-inch nonstick skillet over moderate heat until hot but not smoking, then fry ham in 4 batches, turning occasionally, until crisp and a shade darker, about 1 minute.
Transfer to paper towels to drain.
Using a cheese plane or vegetable peeler, shave 32 small pieces of cheese from wedge. (Each piece should be about 1 inch square.) Top each ham chip with 1/8 teaspoon quince preserves, then press cheese squares into preserves.
*Available at specialty foods shops.
**Available at The Spanish Table (206-682-2827; spanishtable.com).
Cheese can be shaved 4 hours ahead and chilled, loosely covered, on a platter. Ham can be fried 2 hours ahead and kept, uncovered, at room temperature.
