Haptic devices providing various sensations have multiple applications spanning over many fields such as surgical training, robot-assisted minimal invasive surgery (MIS), military, space, and underwater exploration. Most of the existing haptic interfaces lack the capability to effectively replicate the remote environment due to the intricacies involved in providing all necessary sensations simultaneously. In this paper, a novel haptic device with three degrees of freedom (DOF) is developed to render high-fidelity touch sensations like stiffness, texture, shape, and shear concurrently. The proposed haptic device consists of a spherical segment affixed with an array of texture surfaces based on the virtual/remote environment. The device can move in 3-DOF, namely, the pitch, roll, and vertical motion. The haptic interface provides kinesthetic cues like stiffness, shape, and environmental shear and tactile cues like texture by combining the movements of the three actuators along with the segmented housing. A systematic kinematic analysis of the proposed design is presented. The performance is enhanced by implementing the hybrid control methodology that switches between impedance and position control, thus making the interaction realistic and immersive. Experiments have been performed on the developed haptic device, and the results demonstrate its accuracy in reproducing various modalities of haptic feedback of the virtual/remote environment.