The word translated prince in the Greek is archon which in the LXX is used in several different ways, it ultimately means to be in charge of, in the sense of a leader, or the first in command.
Who is therefore the first in command and in charge of this world? And more importantly how did he attain this position?
“in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience—”
The text from which the question was asked gives some clues
“I will no longer talk much with you, for the ruler of this world is coming. He has no claim on me, but I do as the Father has commanded me, so that the world may know that I love the Father. Rise, let us go from here.”
In OT understanding if you gave your allegiance to another god by offering them worship, sacrifice or doing their bidding, such as the lying prophets of Ahab bearing false witness, then the spirit to whom you have given legal jurisdiction to, now has power to appeal in the divine council to act on you. 1 Kings 22
Jesus makes the point that this prince/ruler has NO claim on Him but that Jesus will allow Himself to be subjected to this ruler as the Father has commanded Jesus to do.
“Then Satan entered into Judas called Iscariot, who was of the number of the twelve. He went away and conferred with the chief priests and officers how he might betray him to them.”
In this case Judas fits the Ephesians 2:2 qualifications and being a son of disobedience and the ruler having claim on Judas entered into Judas to execute his plan of capturing Jesus which would later mean execution on the cross.
Who is this prince of the world?
In English it’s satan, but his name means accuser. When he presented himself before the divine council in Job 1&2 the accuser could only do as God allowed him to do to Job. In this case the Father commanded Jesus to allow Himself to be captured. “Not my will but your will be done”.
How did the accuser get to be the ruler of the WORLD?
Also in OT understanding the nations were divided among the sons of God
“When the Most High gave to the nations their inheritance, when he divided mankind, he fixed the borders of the peoples according to the number of the sons of God.”
Each nation received as was allotted to them. However in time these sons of God corrupted themselves and stop being intermediaries between the God most High and their respective human people
“God has taken his place in the divine council; in the midst of the gods he holds judgment: “How long will you judge unjustly and show partiality to the wicked? Selah”
They started to corrupt themselves and were punished by having their immortality stripped from them. Meaning they will be sent to damnation in hell.
These corrupted sons of God who later became the gods of the nations consolidated their powers in their respective kingdoms by giving it to the accuser or satan
And satan says this much himself.
“And the devil took him up and showed him all the kingdoms of the world in a moment of time, and said to him, “To you I will give all this authority and their glory, for it has been delivered to me, and I give it to whom I will.”
So that is how the archon of this world was able to be the prince/ruler or this world
The nations were divided among the gods, these gods corrupted themselves but the people remained subjected to their gods and these gods gave their allegiance to the accuser of satan who is the prince of this world and is only able to have claim on the children of disobedience but if God allows His own children then he has legal claims on them too with limitations.
But Jesus has already paid to restore the whole of Creation and will ultimately do just that. Right now the powers of the air are trying to buy time and delay their inevitable damnation in hell fire.