  We consider a Dice model with Dirac cones intersected by a topologically flat
band at the charge neutrality point and analyze the inelastic scattering of
massless pseudospin-1 particles on a circular, gate-defined, oscillating
barrier. Focusing on the resonant scattering regime at small energy of the
incident wave, we calculate the reflection and transmission coefficients and
derive explicit expressions for the time-dependent particle probability,
current density and scattering efficiency within (Floquet) Dirac-Weyl theory,
both in the near-field and the far-field. We discuss the importance of sideband
scattering and Fano resonances in the quantum limit. When resonance conditions
are fulfilled, the particle is temporarily trapped in vortices located close to
edge of the quantum dot before it gets resubmitted with strong angular
dependence. Interestingly even periodically alternating forward and backward
radiation may occur. We also demonstrate the revival of resonant scattering
related to specific fusiform boundary trapping profiles.
