Tie cinnamon, cloves, and allspice in a cheesecloth bag.
Combine peaches and water in a flat-bottomed kettle; cover and simmer 10 minutes. Add sugar and spice bag. Cook over low heat, stirring occasionally, until sugar dissolves. Bring to a rolling boil, stirring constantly, until mixture registers 220° on a candy thermometer or until mixture sheets from a cold metal spoon. Remove from heat, and skim off foam with a metal spoon; discard spice bag.
Quickly ladle jam into hot sterilized jars, leaving 1/4-inch headspace. Cover at once with metal lids, and screw bands tight. Process jam in boiling water bath 10 minutes.