Propagation of ion acoustic waves (IAWs) and collision of double-, triple-, and quadruple IAWs have been studied in a magnetized plasma system consisting of cold ions and degenerate electrons. It is considered that the ions are inertial and non-degenerate while the electrons are degenerate and non-inertial. The reductive perturbation method is used to derive Zakharov and Kuznetsov (ZK) equation. The multi-soliton solutions of ZK equation are derived using the Hirota bilinear method. The consequences of external periodic force and exchange-correlation potential on the propagation and overtaking collision of ion acoustic (IA) ZK-solitons are investigated taking into account the plasma parameters as observed in astrophysical objects. The considered quantum fluid model is valid for astrophysical conditions in non-relativistic degenerate plasmas where the plasma density and magnetic field strength are 〖10〗^26≤n_0≤〖10〗^29 cm^(-3) and 〖10〗^6≤B_0≤〖10〗^9 G, respectively. It is found that, the amplitude and width of theIAZK-solitons are modified due to the periodic force and exchange-correlation potential. It is also found that the large amplitude solitons always overtake the smaller one.