The specific receptors for neurotransmitters in a synapse are present on :

Neurotransmitters are released from the synaptic vesicles of the pre-synaptic neuron into the synaptic cleft.

These neurotransmitters bind to specific receptors present on the post-synaptic membrane.

This binding opens ion channels, generating a new action potential in the post-synaptic neuron.

Answer: Post-synaptic membrane