Could you please write me a science fiction short story about the coming of darkness to the people of a planet ordinarily illuminated by sunlight at all times in the style of Isaac Asimov?
Certainly. Here's a short science-fiction story set on a hypothetical planet called "Athens" that is normally illuminated by sunlight:

The Athens System
By Isaac Asimov

    Once there was a world known as Athens, which orbited its star with ease and grace for billions of years. Its inhabitants lived lives filled with peace and prosperity, their society based upon laws created long ago by ancient philosophers who had studied the stars. Their civilization thrived thanks to an abundance of natural resources, including metals mined from deep within the earth, precious stones found throughout the landscape, and fresh water flowing from nearby streams and rivers. They were also blessed with unparalleled technology, able to harness powerful energy sources like nuclear fission reactors and fusion generators, making them the most advanced species ever known.

    But one day, without warning or provocation, the Athenians awoke to find themselves in total darkness. All they could see was blackness stretching endlessly before them, punctuated only occasionally by tiny glimmers of reflected light, like distant fireflies. The night sky above glowed an eerie red and orange, but even this faded away after a few moments. There were no more moons to cast shadows or planets to provide some measure of light, leaving the once bright sun a dim, insignificant yellow speck in comparison. The air itself seemed thickened, as if it contained particles too large to be breathed easily. And when the lights came back on, the citizens noticed something strange about those around them—their vision had been altered somehow, so that everything appeared both brighter and dimmer than usual. Some said they saw things moving slowly against the background of the blackest night; others swore they heard whispers carried on drafts of cool breeze. It would take many generations for scientists to discover what truly happened, and another thousand years still for anyone to fully understand the implications.