This dataset contains the information on our recent work on multilevel magnetic synapses for neuromorphic applications and all the relevant data files. In the present work, we exploit voltage-driven nitrogen ion motion in transition metal nitride (CoFeN) thin films (i.e., nitrogen magneto-ionics) to emulate biological synapses. In the proposed device, we have realized distinct multilevel non-volatile magnetic states for analog computing and multi-state storage. Moreover, essential synaptic functionalities of the human brain have been successfully simulated. The device exhibits an excellent synapse with a remarkable retention time (∼ 6 months), high switching ratio and large endurance (∼103), for hardware implementation of NC. This research provides new insight into exploiting magneto-ionic-based synaptic devices for spin-based neuromorphic systems.