 The study reports the experimental realization of order, three exceptional lines, EL3, embedded in order, two exceptional surfaces, ES2, in a three-dimensional periodic synthetic momentum space, which exhibits intriguing spectral topology. The winding number associated with the resultants of the Hamiltonian is used to detect only the EL3 and diagnose the topological currents carried by them, allowing for the prediction of their evolution under perturbations. The study also reveals the connection between the intersection multiplicity of the resultants and the winding of the resultant field around the EPS and generalizes the approach for detecting and topologically characterizing higher-order EPS. This article was offered by Wei Yuan-Tang, Kuon-Ding, and Guan Song-Ma.