OPTION A: Thousands of geosynchronous orbital habitats
Our own world is surrounded by over 2000 satellites but most are so small you cannot see them with your naked eye. Habitats on the other hand would be large enough to see from the ground. The habitats would also twinkle because they rotate to maintain artificial gravity. Their light would mostly be the sun reflecting off of them much like the moon does, but they could use a series of reflector dishes to shine sun light on them even in the planet's shadow so that they can get 24/7 sunlight to power thier solar arrays. This way they never become eclipsed by the planet.
Your world could have once been home to a near future level civilization that experienced a nuclear war or something similar. Some people fled into underground bunkers to survive while others went into space. After a few hundred years, your underground people came back above ground to see a star lite sky while your space people decided to stay in space.
OPTION B: Use a celestial wheel
Another option is that your planet is tidally locked and very close to the star making it uninhabitable. So, eons ago, a space faring race came along and installed a firmament like mega-structure that rotates around the world to give it a day-night system. During the day you have 1 large hole that passes over the the world giving you an apparently normal day cycle, then at night your other side is exposed to the nearby sun letting just small pinholes of light through giving the appearance of stars.
This would more closely resemble stars I think because you would get your sidereal rotation, but it only works if you are in the right place on the planet. As you move away from the world's "center" the sky would become darker until you get to the backside which would be shrouded by eternal darkness & arctic coldness.