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``Extremely red quasars'' (ERQs) are a non-radio-selected, intrinsicallyluminous population of quasars at cosmic noon selected by their extremely redcolour from rest-frame UV to mid-IR. ERQs are uniquely associated withexceptionally broad and blueshifted [\ion{O}{III}]\,$\lambda$5007 emissionreaching speeds $>$6000\,km\,s$^{-1}$. We obtained laser-guided adaptive opticsintegral-field spectroscopic observations using Keck/OSIRIS and Gemini/NIFS ofa sample of 10 ERQs with bolometric luminosities(10$^{47.0}$\textendash10$^{47.9}$)\,erg\,s$^{-1}$ at$z\sim$~(2.3\textendash3.0). The goal is to measure the sizes andspatially-resolved kinematics of the [\ion{O}{III}]-emitting regions. We studythe surface brightness maps and aperture-extracted spectra and model thepoint-spread functions. We identify signs of merger activities in the continuumemissions. We identify physically distinct [\ion{O}{III}] kinematic componentsthat are bimodal and respectively trace ERQ-driven outflows of velocitydispersion $\gtrsim$250\,km\,s$^{-1}$ and dynamically quiescent interstellarmedia. We find that the ERQ-driven ionized outflows are typically at$\sim$1\,kpc scales whereas the quiescent ionized gas extend to a few kpc.Compared to other luminous quasars the extremely fast ERQ-driven [\ion{O}{III}]outflows tend to be more compact, supporting the notion that ERQs are in ayoung stage of quasar/galaxy evolution and represent systems with uniquephysical conditions beyond orientation differences with other quasarpopulations. The kinematically quiescent [\ion{O}{III}] emissions in ERQs tendto be spatially-resolved but less extended than in other luminous quasars,which can be explained by global and patchy dust obscuration. The hint ofionization cones suggests some of the obscuration can be partially explained bya patchy torus.

[\ion{O}{III}]\,$\lambda$5007 emissions in extremely red quasars (ERQs) are compact