Is it permissible to work as a programmer for supermarket software that sells alcohol, knowing that the programming is for information and numbers related to products and has no direct connection to alcohol? And is it permissible to remain in the job for three months to pay off the penalty clause if the work is forbidden?

Drinking alcohol, selling it, buying it, transporting it, and any assistance related to it are forbidden. Those who engage in these acts have been cursed in the Hadith. Therefore, if your work involves writing or arranging anything related to alcohol, it is not permissible for you to do so. However, if you can avoid dealing with alcohol by having someone else do it, then there is no harm. They are not obliged to pay you three months' salary, because your leaving the work is due to their transgression against the law of Allah. If you cannot find a way to get rid of them, and you do not have the money to pay the amount, and this would result in significant harm such as imprisonment, then you are compelled to work with them for three months. But if not paying the money does not result in significant harm, then do not work with them.