In this paper we have made use of reductive perturbation technique (RPT) and carried out homotopy analysis method (HAM) to investigate the effect of exchange correlation and quantum diffraction on the electrostatic waves in quantum magnetoplasma. We have derived a nonlinear Schrödinger equation (NLSE) by using RPT that describes the spatiotemporal evolution of an initial waveform. Apart from this technique, we have made use of HAM to second our initial findings. It has been shown that both quantum diffraction $H$ and parameter streaming velocity $u_0$ have significant effects in determining the stability criteria and the growth or decay of any instability created therein. The stable parametric regimes are crucial from the experimental point of view as well.