The level states of the nucleus ¹²⁴Cs have been populated through the ¹¹⁶Sn(¹¹B,3n) reaction at a beam energy of 45 MeV, provided by the HI-13 tandem accelerator of the China Institute of Atomic Energy. A number of low-lying states are constructed. The level states in the πh_11/2⊗νg_7/2 side band are extended down to lower spin by one hour. The level energies and spins in the rotational bands are determined through the establishment of various connections, which confirm the spin assignment of the yrast band in ¹²⁴Cs based on excitation energy systematics. It is revealed that with the present spin assignment, the πh_11/2⊗νg_7/2 side band shows signature inversion at low-spin region and the inversion occurs at a spin of about 16ℏ. PACS:  21. 10. Re, 23. 20. Lv, 27. 60. +j, 29. 30. Kv