Prepare jars. Wash the jars with hot, soapy water. Then, add them to a waterbath canner. Fill the canner with water until the jars are fully submerged. Place over medium heat and cover. Add the rings and lids to a saucepan with water placed over medium-low heat and allow to simmer.
Slice peppers. Wash the banana peppers and slice them into rings. Discard the stems and seeds according to your preference for heat.
Make brine. Combine vinegar, water, canning salt, and sugar in a large pot. Bring to a boil, stirring to dissolve the salt and sugar.
Pack the jars. Place 1 clove of garlic, 1 teaspoon of mustard seeds, and ½ teaspoon of celery seeds into each hot jar. Pack the sliced banana peppers tightly into the jars, leaving ½ inches of headspace.
Fill jars with brine. Ladle the hot brine over the peppers, maintaining a ½ inch headspace. Remove air bubbles with a bubble remover or spatula. Wipe the jar rims with a clean moist towel. Place the lids and rings on top and tighten the rings until they are fingertip-tight.
Process jars. Transfer the jars to waterbath canner. Make sure the jars are fully submerged with 1-2 inches of water over the jars. Bring the canner to a boil and process for 10 minutes.
Cool. Remove the jars from the canner and let them cool on a towel or cooling rack for 24 hours without moving them. Check the seals, label them, and store them in a cool, dark place for up to a year.
Serve. Enjoy your canned banana peppers on sandwiches, in salads, or as a tangy addition to your favorite dishes.