Building a Radio AGN Sample from Cosmic Morning -- The Radio High-Redshift Quasar Catalog (RHzQCat): I. Catalog from SDSS Quasars and Radio Surveys at $z > 3$

Abstract: Radio-loud high-redshift quasars (RHRQs) provide crucial insights into the evolution of relativistic jets and their connection to the growth of supermassive black holes. Beyond the extensively studied population at $z \ge 5$, the cosmic morning epoch ($3 \lesssim z \lesssim 5$) marks the peak of active galactic nucleus (AGN) activity and black hole accretion, yet remains relatively unexplored. In this work, we compiled the radio high-redshift quasar catalog (RHzQCat) by cross-matching the SDSS DR16Q catalog with four major radio surveys -- FIRST,NVSS, RACS, and GLEAM. Our tier-based cross-matching framework and visual validation ensured reliable source identification across surveys with diverse beam sizes. The catalog included 1629 reliable and 315 candidate RHRQs, with radio luminosities uniformly spanning $10^{25.5}$ -- $10^{29.3}$ W Hz$^{-1}$. About 95\% of the confirmed sources exhibited compact morphologies, consistent with Doppler-boosted or young AGN populations at high redshifts. Our catalog increases the number of known RHRQs at $z\ge3$ by an order of magnitude, representing the largest and most homogeneous catalog of radio quasars at cosmic morning, filling the observational gap between the early ($z>6$) and local Universe. It provides a robust reference for future statistical studies of jet evolution, AGN feedback, and cosmic magnetism with next-generation facilities such as the Square Kilometer Array (SKA).