Final answer:
The organ situated beside the vomerine teeth is Jacobson's organ or the vomeronasal organ, responsible for detecting pheromones.
Step-by-step explanation:
The organ located on either side of the vomerine teeth is Jacobson's organ, also known as the vomeronasal organ (VNO). Jacobson's organ is a tubular, fluid-filled olfactory organ present in many vertebrate animals that is adjacent to the nasal cavity. It is highly sensitive to pheromones and plays a significant role in the detection of these chemical substances. This organ is connected to the nasal cavity by a duct, which allows pheromone molecules dissolved in the mucosa of the nasal cavity to enter the VNO and bind with specialized pheromone receptors. In response to pheromones, many animals display the flehmen response, which is a curling of the upper lip to help pheromone molecules enter the VNO.