While the grasping capability of robotic grippers has shown significant development, the ability to manipulate objects within the hand is still limited. One explanation for this limitation is the lack of controlled contact variation between the grasped object and the gripper. For instance, human hands have the ability to firmly grip object surfaces, as well as slide over object faces, an aspect that aids the enhanced manipulation of objects within the hand without losing contact. In this letter, we present a parametric, origami-inspired thin surface capable of transitioning between a high friction and a low friction state, suitable for implementation as an epidermis in robotic fingers. A numerical analysis of the proposed surface based on its design parameters, force analysis, and performance in in-hand manipulation tasks is presented. Through the development of a simple two-fingered two-degree-of-freedom gripper utilizing the proposed variable-friction surfaces with different parameters, we experimentally demonstrate the improved manipulation capabilities of the hand when compared to the same gripper without changeable friction. Results show that the pattern density and valley gap are the main parameters that effect the in-hand manipulation performance. The origami-inspired thin surface with a higher pattern density generated a smaller valley gap and smaller height change, producing a more stable improvement of the manipulation capabilities of the hand.