DANIEL 1:1
 

IN THE third year of the reign of Jehoiakim king of Judah, Nebuchadnezzar king of Babylon came to Jerusalem and besieged it. [Daniel 1:1 AMPC]

In the third year of the reign of Jehoiakim king of Judah, Nebuchadnezzar king of Babylon came to Jerusalem and besieged it. [Daniel 1:1 NKJV]

According to this Bible verse above, the 3rd year reign of Jehoiakim as king over Judah was also the year Nebuchadnezzar, king of Babylon, came and besieged Jerusalem. But according to this Bible verse below, the 4th year reign of the same Jehoiakim as king over Judah was the first year of Nebuchadnezzar as king over Babylon.

This is the message that came to Jeremiah in the fourth year of Jehoiakim, son of Josiah, king of Judah, which was the first year of Nebuchadnezzar king of Babylon. It concerned all the people of Judah. [Jeremiah 25:1 FBV]

The third year of Jehoiakim kingship over Judah was both the year of Nebuchadnezzar's ascending the throne of Babylon and the year of the same Nebuchadnezzar's besieging Jerusalem in warfare. It sounds as if Nebuchadnezzar immediately advanced into international warfare immediately he became king, but a source from the book of "Daniel's Prophecies" (contemporary of our times, but author unknown to me at the time of writing this) states:

"Jehoiakim reigned from 609-598 B.C. and “did that which was evil in the sight of the Lord” 2 Chronicles 36:5. It was in his 3rd year, 606 B.C., that Nebuchadnezzar came and besieged Jerusalem, in which time Nebuchadnezzar took some of the vessels of the temple of the Lord and some of the inhabitants, Daniel and his three friends included.

It would be interesting to note that during this time king Nabopolassar, Nebuchadnezzar’s father, died leaving the throne naked. Nebuchadnezzar receiving word endeavoured to return to Babylon, in the land of Shinar (Genesis 10:10) to claim it before another did. He rode approximately 700 km’s, across the Syrian Desert, over 22-23 days and claimed the throne and kingship."