Sterilize jars and lids in boiling water for at least 5 minutes.

Bring apples, water, and butter to a boil in a large pot. Reduce heat to low, cover, and simmer until apples are softened, about 8 minutes. Mix in brown sugar, white sugar, pectin powder, and butter flavoring. Bring to a full rolling boil, stirring often. Cook at a boil for 2 minutes without stirring.

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

Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower the jars into the boiling water using a holder. Leave a 2-inch space between the jars. Pour in more boiling water if necessary to bring water level to at least 1 inch above the tops of the jars. Bring water to a rolling boil, cover the pot, and process for 15 minutes.

Remove the jars from the stockpot and place onto a cloth-covered or wood surface, several inches apart, until cool. Once cool, press the top of each lid with a finger, ensuring that the seal is tight (the lid does not move up or down at all). Let stand for 8 hours to overnight before use. Store in a cool, dark area; refrigerate opened jars.