Fill the water bath canner and start heating it with the jars inside before you begin cooking.
Wearing gloves, stem the jalapeños, split them, scrape out the seeds and membranes, and chop them finely. Wash the cutting board and knife before moving on.
Peel the peaches with a paring knife, or dip them in boiling water for about 1 minute and slip off the skins. Pit and chop them.
Crush the peaches with a potato masher, leaving some texture.
Combine the crushed peaches, jalapeños, water, cider vinegar, and lemon juice in a 5 to 6 quart pot.
Bring to a boil, then reduce the heat and simmer for 20 minutes, stirring often so the fruit doesn't scorch.
Stir in the powdered pectin and bring back to a boil over high heat, stirring constantly.
Add the sugar all at once and stir until it dissolves.
Bring to a full rolling boil that doesn't stop when stirred, and boil hard for exactly 2 minutes, stirring constantly.
Remove from the heat and skim off the foam.
Ladle the hot jam into the warm jars, leaving 1/4 inch headspace. Remove air bubbles, wipe the rims, and apply the lids and bands fingertip tight.
Process half pints or quarter pints in a boiling water bath canner for 10 minutes, adjusting for altitude (see notes).
Turn off the heat and let the jars rest in the canner for 5 minutes, then lift them onto a towel.
Cool undisturbed for 12 to 24 hours, then check the seals, remove the rings, and store in a cool, dark place.