Briefly scald the kumquats, immediately rinse with ice-cold water and dry.
Quarter lengthwise, remove the seeds and slice the fruit crosswise. Divide the slices among 5 prepared 250 ml twist-off glasses. Peel and finely chop the ginger.
Mix two tablespoons of sugar and Gelfix, bring to a boil with apple juice, ginger and the lime juice, stirring constantly. Add the remaining sugar and bring to a boil. Stir diligently and boil for 3 minutes (as indicated on the Gelfix bag) until bubbly and pour into the jars. Immediately seal the jars and place on the lid. Turn the jars several times at short intervals to distribute the fruit. When the kumquat season is over, you can cook zest of untreated orange peel as a substitute.