Inspect 5 half-pint jars for cracks and rings for rust, discarding any defective ones. Immerse in simmering water until jelly is ready. Wash new, unused lids and rings in warm soapy water.

Combine 1/2 cup sugar and pectin in a bowl; transfer to a saucepan.

Stir blackberry juice, green jalapeño, and red jalapeño into pectin mixture; bring to a boil over medium-high heat. Add remaining 3 1/2 cups sugar; return to a rolling boil until sugar has fully dissolved, about 1 minute. Off heat, stir to remove bubbles and foam, about 5 minutes.

Pack jelly into hot, sterilized jars, filling to within 1/4 inch of tops. Run a clean knife or thin spatula around insides of jars to remove any air bubbles. Wipe rims with a moist paper towel to remove any residue. Top with lids and screw rings on tightly.

Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 10 minutes or according to your local extension.

Remove jars from the stockpot and let rest, several inches apart, for 12 to 24 hours. Press centers of lids with a finger to ensure lids do not move up or down. Remove rings for storage and store in a cool, dark area. Refrigerate jelly after seal is broken.