We present the study of the superconducting order parameter in single crystals of alkali metal EuCsFe \(_4\) As \(_4\) pnictide belonging to the novel 1144 family, turning to the superconducting state in the stoichiometric composition at critical temperature \(T_c \approx 37\) K, and showing an antiferromagnetic ordering below \(T_c\) . In the superconducting state, using incoherent multiple Andreev reflection effect spectroscopy of superconductor-thin normal metal-superconductor (SnS) junctions, we show a multiple-gap superconductivity with possibly anisotropic large SC gap with an extended s-wave symmetry, and isotropic small SC gap. We directly determined the magnitudes, characteristic ratios, and temperature evolution of the superconducting gaps. The latter are found to be typical for a superconductor with rather weak interband interaction between SC condensates in the k-space.