Any process that modulates the establishment or extent of the postsynaptic membrane potential, which is generated by changes in the membrane potential of the post synaptic neuron that receives information at a synapse. The presynaptic neuron releases neurotransmitters into the synaptic cleft which bind to receptors on the postsynaptic neuron. After being bound by the neurotransmitters, these receptors can open or close an ion channel, allowing ions to enter or leave the cell and therefore altering the membrane potential of the postsynaptic neuron.