Odd-even effects, the non-monotonic dependency of physical properties on odd/even structural units, are widely observed in homologous series of crystalline materials. However, such alternation is not expected for molecular amorphous materials. Herein, we report the synthesis of a class of network-forming ionic glasses using multivalent ammonium cations and citrate anions. The glass transition temperatures of these amorphous solids show an alternating pattern with increasing backbone length. To understand the phenomenon's molecular origin, we performed incoherent elastic neutron scattering measurements of the nanosecond atomic dynamics. Our results suggest that the molecules' mobility, and thus the glass transition temperature, correlates with their structural symmetry.