Dynamics of an electron beam head-on colliding with an ultraintense focused ultrashort circularly-polarized laser pulse are investigated in the quantum radiation-dominated regime. Generally, the ponderomotive force of the laser fields may deflect the electrons transversely, to form a ring structure on the cross-section of the electron beam. However, we find that when the Lorentz factor of the electron $gamma$ is approximately one order of magnitude larger than the invariant laser field parameter $xi$, the stochastic nature of the photon emission leads to electron aggregation abnormally inwards to the propagation axis of the laser pulse. Consequently, the electron angular distribution after the interaction exhibits a peak structure in the beam propagation direction, which is apparently distinguished from the ring-structure of the distribution in the classical regime, and therefore, can be recognized as a proof of the fundamental quantum stochastic nature of radiation. The stochasticity signature is robust with respect to the laser and electron parameters and observable with current experimental techniques.
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