Hot-pack method
Cook tomatoes, celery, onions, sweet peppers, and hot red peppers until soft, about 30 minutes.
Press through a food mill or sieve and cook until reduced by about one-half, about 45 minutes.
Place peppercorns in a spice bag. Add the bag, garlic, sugar, mustard, paprika, salt, hot pepper sauce, cayenne, and 5% vinegar. Cook slowly, stirring frequently, until ketchup consistency, about 1 1/2–2 hours. Remove the spice bag.
Fill hot half-pint or pint jars, leaving 1/2-inch headspace. Remove air bubbles, adjust headspace, wipe rims, and apply lids.
Process in a boiling-water canner for 20 minutes at 0–1,000 ft, 25 minutes at 1,001–3,000 ft, 30 minutes at 3,001–6,000 ft, or 35 minutes above 6,000 ft.