In this research, the electronic and thermodynamic properties of the planer and buckled silicene monolayer under an external magnetic field and doping using the tight-binding (TB) model and the Green function approach are investigated. Also, the dependence of the electronic heat capacity and magnetic susceptibility with temperature, external magnetic field, electron, and hole doping for the planer and buckled silicene monolayer is calculated. Our numerical calculation exhibits that the planer and buckled silicene monolayer have a zero band gap. We find that the electronic heat capacity increases (decreases) by applying an external magnetic field, and electron and hole doping at lower (higher) temperatures due to the increase in the thermal energy (scattering and collision) of the charge carriers. Finally, we observe that the planer and buckled silicene monolayer is antiferromagnetic, which is changed to the ferromagnetic phase when an external magnetic field and doping are applied, which makes the silicene monolayer suitable for spintronic applications.