Final answer:
Fentanyl is the opioid that has no effect on the sphincter of Oddi.
Step-by-step explanation:
The opioid that has no effect on the sphincter of Oddi is Fentanyl. The sphincter of Oddi is a muscular valve that controls the flow of bile and pancreatic juice from the common bile duct and pancreatic duct into the small intestine. While opioids like Morphine, Codeine, and Tramadol can cause constriction of the sphincter of Oddi, Fentanyl has been shown not to have the same effect.