<p>This manuscript presents a detailed investigation of the complexity of cylindrically symmetric fluid distributions influenced by an electric field in the formalism of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(f(R, L_{m}, T)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo>,</mo> <msub> <mi>L</mi> <mi>m</mi> </msub> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> theory. The analysis begins with the consideration of an anisotropic charged fluid configuration, where modified field equations are formulated after using the relations between internal curvature and the conformal tensor. We explore the mathematical structure of the C-energy and Tolman mass and examine their connection with the conformal tensor. The impact of anisotropic pressures and varying energy densities is thoroughly assessed. Furthermore, the orthogonal splitting of the Riemann curvature tensor yields structure scalars, with particular focus on the scalar factor, which serves as a measure of complexity associated with anisotropic matter. It is shown that for homogeneous energy density, the complexity factor vanishes. Significant conclusions are drawn regarding the behavior of the Weyl scalar, Tolman mass, and complexity factor under the influence of the more degrees of freedom in our considered gravity. The role of the vanishing complexity condition is also emphasized in obtaining physically viable solutions.</p>