Kagome lattices host rich magnetic, topological, and transport phenomena owing to their geometric frustration and strong spin correlations. Here we present a systematic neutron scattering study of the kagome metal Y_(0.5)Fe₃Sn₃, which orders into a collinear c-axis antiferromagnetic (AF) state below T_N = 551 K. An additional anomalous Hall effect (AHE) contribution beyond the conventional magnetization-scaling response is observed well below T_N under an in-plane magnetic field B ∥ ab. Elastic neutron scattering demonstrates that the Fe moments preserve their collinear c-axis AF alignment down to 1.5 K at zero field. Inelastic neutron scattering reveals a distinctive Y-shape spin excitation dispersion exhibiting a two-gap structure below 10 meV, likely arising from two nondegenerate spin-wave branches. Polarized neutron measurements further show that the low-temperature spin excitations are strongly anisotropic: the in-plane component M_ab dominates while the c-axis component M_c is nearly absent. Upon warming, M_c gradually grows markedly but remains much weaker than M_ab even at 300 K. We propose that the unconventional AHE originates from a nonzero scalar spin chirality induced by field-driven spin canting either in the static or dynamic configurations due to gapless excitations. These findings establish the collinear AF kagome metal Y_(0.5)Fe₃Sn₃ as a platform for chirality-driven AHE without spontaneous spin reorientation.