Exploration of the topological quantum materials with electron correlation is at the frontier of physics, as the strong interaction may give rise to new topological phases and transitions. Here we report that a family of kagome magnets RMn_{6}Sn_{6} manifest the quantum transport properties analogical to those in the quantum-limit Chern magnet TbMn_{6}Sn_{6}. The topological transport in the family, including quantum oscillations with nontrivial Berry phase and large anomalous Hall effect arising from Berry curvature field, points to the existence of Chern gapped Dirac fermions. Our observation demonstrates a close relationship between rare-earth magnetism and topological electron structure, indicating the rare-earth elements can effectively engineer the Chern quantum phase in kagome magnets.