The precedent set in this decision no longer affects citizens in any way because the precedent has since been overturned. Dennison was decided in 1860. However, it was overturned in 1987.
During the time that it was in force, the precedent set in Dennison could have affected only a very few citizens. This decision held that the governor of one state could not be compelled by a federal court or by Congress to extradite a person from their state to another. In this case, Kentucky wanted someone extradited from Ohio for helping a slave to escape. The Supreme Court held that the person should be returned to Kentucky for trial but that the federal government lacked the power to compel Ohio’s governor to extradite.
This would not have affected very many citizens. It would only have affected those citizens who committed a crime in one state that another state did not think was serious enough to warrant extradition. This could have happened in pre-Civil War times when there was such controversy over slavery. However, it is unlikely that many governors would have protected people from extradition for the general run of crimes that do not have any political significance. Therefore, the precedent did not affect many citizens even when it was in force.
In 1987 this precedent was overturned in Puerto Rico v. Branstad so now extradition is required. Therefore, it no longer impacts any American citizens.