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X-ray and Radio Studies of the candidate Millisecond Pulsar Binary 4FGL J0935.3+0901

4FGL J0935.5+0901, a $γ$-ray source recently identified as a candidate redback-type millisecond pulsar binary (MSP), shows an interesting feature of having double-peaked emission lines in its optical spectrum. The feature would further suggest the source as a transitional MSP system in the sub-luminous disk state. We have observed the source with \xmm\ and Five-hundred-meter Aperture Spherical radio Telescope (FAST) at X-ray and radio frequencies respectivelyfor further studies. From the X-ray observation, a bimodal count-rate distribution, which is a distinctive feature of the transitional MSP systems, is not detected, while the properties of X-ray variability and power-law spectrum are determined for the source. These results help establish the consistency of it being a redback in the radio pulsar state. However no radio pulsation signals are found in the FAST observation, resulting an upper limit on the flux density of $\sim 4\,μ$Jy. Implications of these results are discussed.