We perform a molecular (CO and CN) line observation using the IRAM 30m telescope toward two small regions near the western edge of supernova remnant (SNR) W50/SS 433. CO observation reveals spatial correspondence of two molecular clumps at the local-standard-of-rest (LSR) velocity around +53 km s −1 , with multiwavelength local features of the W50/SS 433 system. One of the two clumps appears to be embedded in a void of diffuse radio and X-ray emission. Toward the two clumps, asymmetric broad-line profiles of the 12 CO lines are obtained, which provide kinematic evidence of the association between the clumps and the jet-related gas. The 12 CO J= 2-1/J= 1-0 line ratios ( 0.9) and the kinetic temperatures (∼ 30 K) of the clumps are distinctively higher than all those of the clumps at other LSR velocities along the same line of sight, which may be physical signatures of the association. We show that the clump coincident with the void can survive the thermal heating if it is surrounded by hot gas, with an evaporation timescale much larger than the age of SNR W50. We also show that the thermal equilibrium in the high-temperature clumps can be maintained by the heating of the penetrating environmental cosmic rays. CN (J = 3/1-1/2) line emission is detected in the two clumps, and the CN abundances derived are much higher than that in the interstellar molecular clouds (MCs) and that in the SNR-interacting MCs.