Is it obligatory for someone who takes antidepressant medication prescribed in the name of his sick father to donate the value of the medicine he took throughout the treatment period?

If the doctor prescribes medicine for you along with your father's medicine so that you can obtain it for free from the entity that provides free medicine to your father, then this is impermissible, and you must repent from it. It is not permissible to give the value of the medicine as charity; rather, it must be returned to the entity from which it was wrongfully obtained, or you must seek forgiveness from its owners. However, if returning it or seeking forgiveness is not possible, then it is permissible to give its value in charity on their behalf.