This paper presents an underactuated design of a robotic hand exoskeleton and a challenge based neurorehabilitation strategy. The exoskeleton is designed to reproduce natural human fingertip paths during extension and grasping, keeping minimal kinematic complexity. It facilitates an impedance adaptation based trigged assistance control strategy by a switching between active non-assist and passive assistance modes. In active non-assist mode, the exoskeleton motion follows the applied fingertip forces based on an impedance model. If the applied fingertip forces are inadequate, the passive assistance mode is triggered. The impedance parameters are updated at regular intervals based on the user performance, to implement a challenge based rehabilitation strategy. A six-week long hand therapy, conducted on four chronic stroke patients results in significant (p-value<0.05) increase in force generation capacity and decrease (p-value<0.05) in the required assistance. Also, there was a significant (p-value<0.05) increase in the system impedance parameters which adequately challenged the patients. The change in the Action-Research-Arm-Test (ARAT) scores from baseline are also found to be significant (p-value<0.05) and beyond the minimal clinically important difference (MCID) limit. Thus the results prove that the proposed control strategy with has the potential to be a clinically effective solution for personalized rehabilitation of poststroke hand functionality.