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In this work, we have studied the spin-dependent ballistic transport and anomalous quantum tunnelling in Bilayer Graphene (BLG) hybrid connected to two Rashba-Zeeman (RZ) leads under an external electric biasing. We investigated the transmission and conductance for the proposed system using scattering matrix formalism and Landauer - Buttiker formula considering a double delta-like barrier under a set of experimentally viable parameters. We found that the transmission characteristics are notably different for up and down spin incoming electrons depending upon the strength of magnetization. Moreover, the transmission of up and down spin electrons is found to be magnetization orientation dependent. The maximum tunnelling and conductance can be achieved by tuning biasing energy and magnetization strength and choosing a material with suitable Rashba Spin-Orbit Coupling (RSOC). This astonishing property of our system can be utilized in fabricating devices like spin filters. We found the Fano factor of our system is 0.4 under strong magnetization conditions while it reduces to 0.3 under low magnetization conditions. Moreover, we also noticed that the transmission and conductance significantly depend on the Rashba - Zeeman effect. So, considering a suitable RZ material, the tunnelling of the electrons can be tuned and controlled.