Controlling the site, size, and shape of group III-nitride quantum dots (QDs) is critical for the development of mass-producible single-photon sources for scalable quantum technologies operable at room temperature. Herein, a methodology is proposed for fabricating high-purity single QD emitters by controlling site-controlled GaN micro-pyramid structures with a high degree of uniformity and symmetry. To achieve a uniformly grown, hexagonally symmetric micro-pyramid array, the H-2/N-2 carrier gas ratio, growth temperature, and V/III ratio are controlled to attain self-limited growth regime and self-limited width at the GaN pyramid apex. A thin InGaN layer is consecutively grown on a pyramid array under the growth condition for enhancing the growth rate anisotropy to hinder the growth of InGaN quantum wells (QWs) at semi-polar facets. As a result, single-photon emission is observed from apex QD with suppressed background side QW emission while maintaining more than 90% high hexagonal QD symmetry over the large area of the wafer.