Margination, a fundamental process in which leukocytes migrate from the flowing blood to the vessel wall, is well-documented in physiology. However, it is still an open question on how the differences in cell size and stiffness of white and red cells contribute to this phenomenon. To investigate the specific influence of cell stiffness, we conduct experimental and numerical studies on the segregation of a binary mixture of artificially stiffened red blood cells within a suspension of healthy cells. The resulting distribution of stiffened cells within the channel is found to depend on the channel geometry, as demonstrated with slit, rectangular, and cylindrical cross-sections. Notably, an unexpected central peak in the distribution of stiffened RBCs, accompanied by fourfold peaks at the corners, emerges in agreement with simulations. Our results unveil a non-monotonic variation in segregation/margination concerning hematocrit and flow rate, challenging the prevailing belief that higher flow rates lead to enhanced margination