We report synthesis and examination of the electronic properties of an isomorphous series of mixed-stack organic charge-transfer complexes, composed of [bis(ethylenedithio)tetrathiafulvalene] (BEDT-TTF)-based electron donors and electron acceptors of halogen-substituted tetracyanoquinodimethanes (TCNQ's). Single crystals of ${(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\ensuremath{-}\mathrm{T}\mathrm{T}\mathrm{F})(\mathrm{M}\mathrm{e}}_{2}\mathrm{TCNQ}),$ (BEDT-TTF)(ClMeTCNQ), and ${(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{O}\ensuremath{-}\mathrm{T}\mathrm{T}\mathrm{F})(\mathrm{C}\mathrm{l}}_{2}\mathrm{TCNQ})$ were investigated as to their crystal structures, and optical and magnetic properties. The intermolecular overlaps between the stacked columns were comparable to the face-to-face overlap between the donor and the acceptor molecules inside the stacks. As seen from the optical and magnetic measurements, the ${(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\ensuremath{-}\mathrm{T}\mathrm{T}\mathrm{F})(\mathrm{M}\mathrm{e}}_{2}\mathrm{TCNQ})$ and (BEDT-TTF)(ClMeTCNQ) complexes were neutral, while the ${(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{O}\ensuremath{-}\mathrm{T}\mathrm{T}\mathrm{F})(\mathrm{C}\mathrm{l}}_{2}\mathrm{TCNQ})$ complex was found to be ionic. Among these complexes, anomalous magnetic properties were observed in the ionic complex of ${(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{O}\ensuremath{-}\mathrm{T}\mathrm{T}\mathrm{F})(\mathrm{C}\mathrm{l}}_{2}\mathrm{TCNQ}).$ ${(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{O}\ensuremath{-}\mathrm{T}\mathrm{T}\mathrm{F})(\mathrm{C}\mathrm{l}}_{2}\mathrm{TCNQ})$ is a magnetic insulator with Curie-Weiss behavior in magnetic susceptibility followed by a sharp drop at around 120 K, which is in sharp contrast to conventional ``spin-Peierls-type'' nonmagnetic mixed-stack ionic compounds.