We study 25–120 GHz electron spin resonance in a quasi-two-dimensional \(S=\) 3/2 antiferromagnet on an isosceles triangular lattice Cs \(_2\) CoCl \(_4\) . Due to the frustration of the exchange interaction along the lateral sides of the triangles, the exchange network may be viewed as a quasi-one-dimensional system of weakly interacting chains. The strong single-ion anisotropy of Co \(^{2+}\) allows a pseudospin \(s=\) 1/2 formulation of the problem. We observe in experiments a well-pronounced temperature crossover from the ESR of individual pseudospins with a g-factor of 3.3 (corresponding well to individual pseudospins s=1/2) to ESR spectrum shifted strongly down in frequency at the temperature range below 1 K. This shifted ESR spectrum corresponds well to the singularity at the lower boundary of the quasi-spinon continuum of an XXZ spin chain in a transverse field, calculated in theory by Bruognolo et al., in Phys Rev B 94:085136, 2016 and by Laurell et al., in Phys Rev Lett 127:037201, 2021.