Bring boiling-water canner, half full with water, to simmer.
Wash jars and screw bands in hot soapy water; rinse with warm water.
Pour boiling water over flat lids in a saucepan off the heat. Let stand in hot water until ready to use. Drain jars well before filling.
Peel and core pineapple. Finely chop and measure exactly 2 cups chopped pineapple into a large, (6-8-quart) pot.
Zest the orange part of the mandarins, avoiding the pith (white part). You can use a zester like this one or a vegetable peeler the thinly slice the zest. Add the zest to the pot with the pineapple.
Peel the mandarins and remove as much of the stringy white pith as possible. No worries if you can’t get some of it off.
Sliced the mandarins in half then chop into small pieces. I like to slice the halves about ¼ inch thick then chop the slices.
As you chop, measure exactly 2 cups of chopped mandarin and add to the pot.
Peel and core the apple and finely chop until you have exactly ½ cup. Add the apple to the pot.
Stir in the pectin. Add butter to reduce foaming.
Bring the mixture to a full rolling boil (that means a boil that doesn't stop bubbling when stirred) over high heat, stirring frequently.
Add the sugar and stir well. Bring the mixture back to a full rolling boil then set a timer for one minute. Continue with the boil, stirring frequently.
After one minute, remove the pot from the heat. Skim off any foam with a metal spoon. Ladle immediately into prepared jars, filling to within ¼ inch of the tops. Wipe jar rims and threads. Cover with two-piece lids. Screw bands tightly.
Place jars on an elevated rack in the canner. Lower rack into canner. (Water must cover jars by 1 to 2 inches. Add boiling water, if necessary.)
Cover; bring water to a gentle boil. Process for 5 minutes.
Remove the jars and place them upright on a towel to cool completely.
After the jars are cool, check the seals by pressing the middle of the lids with a finger.
If lids spring back, lids are not sealed and refrigeration is necessary, otherwise, the marmalade will be shelf stable until opened.