This study explores the plasma-assisted molecular beam epitaxy (PAMBE) growth and characterization of high-quality niobium nitride (NbN) thin films on miscut c-plane sapphire substrates, with the ultimate goal of improving their superconducting properties for potential applications in low microwave noise Josephson junctions and superconducting quantum circuits. Specifically, the study investigates the effects of substrate miscut angles on the critical temperature, coherence length, and critical magnetic field of NbN thin films, providing valuable insights for developing advanced superconducting devices.The research begins with the PAMBE growth of NbN films using the Veeco GENxplor MBE system. The study focuses on achieving cubic $\delta$-phase NbN, known for its superior superconducting properties, with controlled growth parameters such as substrate temperature. Characterization techniques, including X-ray diffraction (XRD) and atomic force microscopy (AFM), are employed to assess the structural properties and surface morphology of the NbN films. Then, the superconducting properties of NbN were measured and examined via the Quantum Design Physical Property Measurement System. For the annealed substrate sample series, the results reveal a monotonic increase in critical temperature and a decrease in coherence length with increasing substrate miscut angle, which is favorable for applications requiring precise control over tunneling properties and critical current. The critical magnetic field also increases with increasing substrate miscut angle, indicating enhanced superconducting stability in high magnetic field environments. At last, the challenges associated with critical temperature and coherence length measurements are discussed.