Can a minor who is US citizen travel back to the United States from Jamaica with a parent on a expired passport ?
Currently, yes. From https://www.iatatravelcentre.com/world.php:
Nationals of the U.S.A. are allowed to enter with an expired passport. This does not apply to emergency passports which must be valid on arrival.
You may want to also call the airline to make sure they're also ok with it.