What is the ruling regarding the money and fish that the driver takes as a "tip" from the owners of fish farms in exchange for transporting fish, with the knowledge of the vehicle owner?

We understand from your question that your father works as a taxi driver. What he receives from fish farm owners is considered in the same category as gifts to employees, which are not permissible unless authorized by the employer. This is due to the prohibition mentioned in authentic hadiths. So, if the car owner permits your father to take what he receives, then there is no objection. But if he does not permit it, then it is not permissible for him to take anything from that.