An adaptive sub-band differential microphone array beamformer is proposed in order to achieve a distortionless response at arbitrary target directions, using two closely-spaced microphones in a hearing aid. Different variations are introduced to have a distortionless response in the target speaker direction. Two of these variations assume a free field environment when designing the beamformer, while two other designs consider the head shadow effect by using Head-Related Transfer Functions (HRTFs), for hearing aid applications. Simulation results show that the four proposed designs can outperform the standard sub-band design from the literature, in terms of back hemisphere noise reduction and target distortion. The results also illustrate the superiority of the HRTF-based designs over the free field-based designs, in terms of target distortion.