The layer of the Badlands that contains reptile fossils but no dinosaur fossils is the White River Formation.

Here's why:

* Dinosaur Extinction: Dinosaurs went extinct around 66 million years ago.

* White River Formation Age: The White River Formation, which is part of the Oligocene Epoch, dates back to between 34 and 23 million years ago.

* Reptile Survival: While dinosaurs disappeared, many other reptile species, like crocodiles, snakes, and turtles, survived and continued to evolve.

Therefore, the White River Formation contains fossils from various types of reptiles that existed long after the extinction of dinosaurs.