This is the only recipe in the Cariadoc's Miscellany that is based on a modern source: A Book of Middle Eastern Food, by Claudia Roden. Sekanjabin is a period drink; it is mentioned in the Fihrist of al-Nadim, which was written in the tenth century. The only period recipe Cariadoc has found for Sekanjabin (in the Andalusian cookbook) is called "Sekanjabin Simple" which omits the mint. It is one of a large variety of similar drinks described in that cookbook.
4 cups sugar
2 1/2 cups water
1 cup wine vinegar
1 handful of mint
Note: You can substitute apple cider vinegar for the wine vinegar.
Dissolve 4 cups sugar in 2 1/2 cups of water; when it comes to a boil add 1 cup wine vinegar. Simmer 1/2 hour. Add a handful of mint, remove from fire, let cool.
Dilute the resulting syrup to taste with ice water (5 to 10 parts water to 1 part syrup). The syrup stores without refrigeration. Flavored syrups intended to be diluted in either hot or cold water before drinking.
A Book of Middle Eastern Food, by Claudia Roden