We present a comprehensive study on the characteristics of electrostatic surface waves in a magnetized quantum plasma half-space. By analytically investigating the system under the influence of quantum diffraction and Fermi pressure, we employ the quantum hydrodynamic model (QHD) and the specular reflection boundary condition at the plasma-vacuum interface to accurately capture quantum effects. We analyze the dispersion relations for two specific cases of magnetic field orientation: parallel and perpendicular to the interface. We numerically plot the dispersion relations and explore the effects of plasma parameters, such as plasma density, cyclotron frequency, and Fermi velocity, on the surface wave behavior. The results show that increasing plasma density and Fermi velocity result in changes in the normalized frequency of surface waves, while an increase in the cyclotron frequency leads to a significant increase in the surface plasmon frequency. Our work provides valuable insights into the behavior of electrostatic surface waves in magnetized quantum plasmas and their potential applications in waveguide structures and other related areas such as signal processing, communication systems, sensing devices, quantum dot devices, nanostructures.