Composite quantum materials are the ideal examples of multifunctional systems which simultaneously host more than one novel quantum phenomenon in physics. Here, we present a combined theoretical and experimental study to demonstrate the presence of an extremely large exchange bias in the range 0.8 T - 2.7 T and a fully compensated magnetic state (FCF) in a special type of Pt and Ni doped Mn$_3$In cubic alloy. Here, oppositely aligned uncompensated moments in two different atomic clusters sum up to zero which are responsible for the FCF state. Our Density functional theory (DFT) calculations show the existence of several possible ferrimagnetic configurations with the FCF as the energetically most stable one. The microscopic origin of the large exchange bias can be interpreted in terms of the exchange interaction between the FCF background and the uncompensated ferrimagnetic clusters stabilized due to its negligible energy difference with respect to the FCF phase. We utilize pulsed magnetic field up to 60 T and 30 T static field magnetization measurements to confirm the intrinsic nature of exchange bias in our system. Finally, our Hall effect measurements demonstrate the importance of uncompensated noncoplanar interfacial moments for the realization of large EB. The present finding of gigantic exchange bias in a unique compensated ferrimagnetic system opens up a direction for the design of novel quantum phenomena for the technological applications.
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