Narrowband Internet of Things (NB-IoT) is the technology developed by 3GPP to bring the connectivity among IoT devices. The main aim of this technology is to improve the coverage and support massive number of IoT devices with long battery life. Coverage is enhanced by data repetitions over an extended period of time. The battery life at the User Equipment (UE) is extended by incorporating long DRX cycles of 10.24 sec. Preserving timing and frequency synchronization under such long repetitions and DRX cycles poses a challenge for NB-IoT. In this paper we propose Narrowband Reference signals (NRS) based tracking of residual timing and frequency offsets. The proposed method assume that the initial synchronization has been carried out using NB Primary (NPSS) and Secondary synchronization (NSSS) signals. The results obtained from the initial synchronization serves as the coarse estimates for the proposed method. Inherent non rapid channel variations across NRS carrying subcarriers of successive OFDM symbols is exploited to estimate residual offsets. The extracted residual offsets from NRS signals of two antenna ports are combined to refine the estimates. The performance results of presented algorithm and its processing time to yield the estimates at -12 dB SNR obtained by computer simulations are presented. © 2018 IEEE.