A clock recovery algorithm (CRA) suitable for non-integer oversampled Nyquist signals with a small roll-off factor (ROF) is appealing to short-reach high-speed inter-datacenter transmission systems which need to cut down the transceiver power consumption and cost by reducing the oversampling factor (OSF) and using cheap low-bandwidth components. However, due to the lack of a suitable timing phase error detector (TPED), CRAs proposed now fail for non-integer OSFs below two and small ROFs close to zero and are not hardware-efficient. To solve these problems, we propose a low-complexity TPED by modifying the time-domain quadratic signal and reselecting the synchronization spectral component. We demonstrate that the proposed TPED, in combination with a piece-wise parabolic (PWP) interpolator, can significantly improve the performance of feedback CRAs for non-integer oversampled Nyquist signals with a small ROF. Numerical simulations and experiments show that, based on the improved CRA, the receiver sensitivity penalty can keep below 0.5 dB when the OSF is reduced from 2 to 1.25 and the ROF is varied from 0.1 to 0.001 for 45 GBaud dual-polarization Nyquist 16QAM signals.