The electron sheath formation in a DC magnetised plasma of modified hollow cathode source is studied. The discharge consists of two plane parallel cathodes and a small cubical anode placed off axis at the center. The argon plasma is produced, and the properties of the plasma in response to the sheath formation near the anode are studied using electrical and optical diagnostics. In particular, the effect of pressure and magnetic field on the discharge parameters, such as discharge current, plasma potential, plasma density, and electron temperature, is studied. The discharge showed an onset of anode glow at a critical applied magnetic field, indicating the formation of electron sheath and a double layer. The discharge current initially decreases; however, it starts to rise again as the anode spot appears on the anode. The critical magnetic field at which the anode glow formation takes place is dependent upon operating pressure and discharge voltage. The transition from ion sheath to electron sheath is investigated in detail by Langmuir probe and spectroscopy diagnostics. The plasma potential near the anode decreases during the transition from ion sheath to electron sheath. The plasma potential locks to the ionization potential of argon gas when anode spot is completely formed. A systematic study showed that during the transition, the electron temperature increases and plasma density decreases in the bulk plasma. The spectroscopy of the discharge showed the presence of strong atomic and ionic lines of argon. The intensity of these spectral lines showed a dip during the transition between two sheaths. After the formation of the anode spot, oscillations of the order of 5–20 kHz are observed in the discharge current and floating potential due to the enhanced ionisation and excitation processes in the electron sheath. The reason for the electron sheath formation at particular magnetic field is attributed to the reduction of the electron flux reaching to the anode in the direction perpendicular to the magnetic field.