In a quasi-one-dimensional S=1/2 antiferromagnet K₂CuSO₄Br₂ we observe experimentally a shift of the boundaries of the spinon continuum caused by a Fermi-liquid interaction of spinons. The spinon interaction parameter originating from their backscattering is determined. In a pseudospin S=1/2 chain-type strongly anisotropic antiferromagnet Cs₂CoCl₄ a croosover from the uncorrelated paramagnetic phase to in-chain correlated regime is detected by the observation of the shift of the electron spin resonance spectrum. This crossover corresponds to a temperature range above the phase transition to the 3D long-range order. The shift of the magnetic resonance frequencies is shown to be consistent with the correlated XXZ spin S=1/2 chains and corresponds well to the theoretical modeling of the spinon spectrum in XXZ chains (P. Laurell, A. Scheie, C. J. Mukherjee, M. M. Koza, M.Enderle, Z. Tylczynski, S. Okamoto, R. Coldea, D. A. Tennant, and G. Alvarez, Phys. Rev. Lett. 127 037201 (2021)).