The correct answer is: A. 15th September, 1950.
The Court of Judicial Commissioner in Himachal Pradesh started functioning regularly on 15th September, 1950. It was established under the Himachal Pradesh Court of Judicial Commissioner Act, 1950. The Court was initially headed by a Judicial Commissioner, who was appointed by the President of India. The Court had jurisdiction over all civil and criminal cases in Himachal Pradesh. In 1972, the Court was upgraded to a High Court.
Option B is incorrect because Himachal Pradesh became a part of India on 15th August, 1948. However, the Court of Judicial Commissioner was not established until 15th September, 1950.
Option C is incorrect because Himachal Pradesh was not a part of India on 16th August, 1948. It became a part of India on 15th August, 1948.
Option D is incorrect because the Court of Judicial Commissioner was not established until 15th September, 1950.