Fussiness is a quality of being overly careful or extremely hard to please. Your dad's fussiness might mean that his spices are organized alphabetically — and that he gets very annoyed if you put them back in the wrong order.
If you like to have things just so before starting your homework — your room tidied, and two pencils on your desk lying parallel to your laptop — that's fussiness. You might also say you're fastidious or detail-oriented. Another kind of fussiness is essentially being picky about what you eat: "My brother's fussiness means we're always stuck eating pasta or pizza for dinner." And parents often describe the cries of an unhappy baby as fussiness, too: "Her fussiness is the worst at midnight."