We establish a connection between motivic cohomology classes over the Siegel threefold and non-critical special values of the degree-four $L\(-function of some cuspidal automorphic representations of \)\text{GSp}(4)\(. Our computation relies on our previous work [ On higher regulators of Siegel threefolds I: the vanishing on the boundary, Asian J. Math. 19 (2015), 83–120] and on an integral representation of the \)L$ -function due to Piatetski-Shapiro.