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Numerous applications in medical diagnostics, cell engineering therapy, and biotechnology require the identification and sorting of cells that express desired molecular surface markers. We developed a microfluidic method for high-throughput and label-free sorting of biological cells by their affinity of molecular surface markers to target ligands. Our approach consists of a microfluidic channel decorated with periodic skewed ridges and coated with adhesive molecules. The periodic ridges form gaps with the opposing channel wall that are smaller than the cell diameter, thereby ensuring cell contact with the adhesive surfaces. Using three-dimensional computer simulations, we examine trajectories of adhesive cells in the ridged microchannels. The simulations reveal that cell trajectories are sensitive to the cell adhesion strength. Thus, the differential cell trajectories can be leveraged for adhesion-based cell separation. We probe the effect of cell elasticity on the adhesion-based sorting and show that cell elasticity can be utilized to enhance the resolution of the sorting. Furthermore, we investigate how the microchannel ridge angle can be tuned to achieve an efficient adhesion-based sorting of cells with different compliance.