What does King Creon want to do about Medea?

King of Corinth. New father-in-law to Jason. Not to be confused with Creon of Sophocles' Theban plays. Creon exiles Medea, fearing that the dangerous witch will seek vengeance against his family. Medea takes advantage of Creon's underestimation of her: she begs for one day to make preparations, and the king grants it. This day is enough fro Medea to destroy Creon and his daughter.

King Creon is almost an ambiguous character.
He sparks the issue in the first place by choosing Jason to wed his daughter. (This gave the opportunity for Jason to look beyond Medea and disguise his motivations for fame by stating that he had his family's "interest at heart".)
Creon also claims to not be a "tyrant in his heart" by letting Medea stay another day, but this decision was brought about by the aims to "protect himself". Ultimately, he abuses the power and authority he has as King to send Medea into exile. Because he sends Medea into exile because he "fear" her not because he intentions are to protect his people etc.
But as a father Creon, has to best intentions to give his daughter security and keep her safe. But his decision for her to marry Jason may be for political benefits.