What is the ruling on taking payment for teaching Islamic sciences, and does this fall under the Hadith: "Whoever learns knowledge by which the Face of Allah Almighty is sought, yet he learns it only to gain some worldly benefit thereby, will not perceive the fragrance of Paradise on the Day of Resurrection"?

It is permissible to take a wage for teaching religious sciences, though it is preferable not to take one if possible. The threat mentioned in the noble Hadith applies only to those who learn knowledge solely for worldly gain. As for someone who learns knowledge for the sake of Allah, and then has no other means of livelihood than teaching, there is no blame upon him.