What is the ruling on inseminating cows in veterinary clinics, and is it considered "asb al-fahl" (the stud fee)?

There is no objection to inseminating cows in veterinary clinics, and this is not considered the forbidden "stud's service" (ʿasb al-faḥl). The prohibition of the "stud's service" is specific to the act of the stud's natural mating itself. As for artificial insemination, it is the effort and expertise of a veterinarian, and it is a work that can be delivered and accomplished. The stud's semen is not exclusively the subject of the contract; rather, the contract is for the veterinarian's effort. And "what is permissible as a تابع (subsidiary/consequence) is not permissible as an مستقل (independent/primary)."