Prep. Heat your canning jars. You can do this by washing them in hot, soapy water and then placing them in a simmering water bath canner for 10 minutes. Keep the jars hot until ready to use. Prepare the lids and bands according to the manufacturer’s instructions.
Combine Relish Ingredients. In a large pot, combine the chopped jalapeños, onion, garlic, apple cider vinegar, white vinegar, sugar, mustard seeds, celery seeds, turmeric, and salt.
Cook. Bring the mixture to a boil over medium-high heat, stirring frequently to dissolve the sugar. Reduce the heat and simmer for 10 minutes, allowing the flavors to meld and the mixture to thicken slightly.
Fill the Jars. Carefully remove the hot jars from the water bath canner using a jar lifter. Place a canning funnel over the mouth of one jar, and ladle the hot relish into the jar, leaving a 1/2-inch headspace. Use a bubble remover tool or a non-metallic spatula to remove any air bubbles by gently inserting it into the jar and moving it around the edges.
Clean rims and place lids. Wipe the rim of the jar with a clean, damp cloth or paper towel to ensure it is free of any relish residue. Place the lid on the jar, then screw on the band until it is fingertip tight.
Process the Jars. Place the filled jars back into the water bath canner, making sure they are covered by at least 1 inch of water. Bring the water to a full, rolling boil. Process the jars in the boiling water for 10 minutes (adjust the time for altitude as needed). After processing, turn off the heat and remove the canner lid. Let the jars sit in the water for 5 minutes to adjust to the temperature change.
Cool. Use a jar lifter to carefully remove the jars from the canner and place them on a towel or cooling rack, making sure they are not touching each other. Allow the jars to cool undisturbed for 12 to 24 hours. Check the seals by pressing down on the center of each lid. If the lid does not pop back, it is sealed properly.
Store. Label your jars with the content and canning date. Store in a cool, dark place. Wait at least 2 weeks for the flavors to develop before using.