In Daniel 11:15, Antiochus III continues his siege campaign spoken of in V 13. Gaza fell in 201 BC after a terrible siege. It can also refer to when Antiochus III forced an Egyptian army to surrender after a siege at Sidon.
Gabriel is reviewing the punishment of the Jews by the king of the north. The king of the south and the Jews were absolutely powerless against the king of the north.
In Verse 16, Roman powers attack the Grecian king of the north in the holy land who fell before the Roman general Pompey in 63 BC. Jerusalem's independence is taken by Rome by Pompey in 63 BC and Rome begins its prophesied rule as depicted in the dream of Nebuchadnezzar in chapter 2 and Daniel's visions in chapters 7 & 8. Jerusalem became a province of Rome in 63 BC.
The Grecian dynasty's prophesied end after 268 years of rule in Palestine. Rome takes control and becomes the king of the north. (It's not until 30 BC that Rome is able to take control of the territory of the king of the south.) Jerusalem never again regains independence. In fact, they are under Roman rule all the way up to 70 AD when Titus destroys the city.
Verse 17: "he shall also..." denotes Rome lead by Julius Caesar who entered with the strength of his whole kingdom. As arrogant as Caesar was, he did as he pleased against the remaining portion of Alexander's kingdom, that being of course, Egypt, Ptolemy XI = king of south.
Ptolemy XI placed his two children, Cleopatra and Ptolemy XII, under guardianship of Rome before his death in 51 BC. Cleopatra came on the scene after Alexander's death.
Caesar corrupted Cleopatra by having her as his mistress and corrupted politically as history proves. After Caesar was assassinated, she tried to join her forces with Marc Antony's to defeat Octavian to merge Egypt and Rome.
Her loyalty remained with her father's kingdom of the south. After his assassination in 44 BC (see verse 19) she and Marc Antony tried to merge Egypt with Rome's growing Empire presently under the rule of Octavian her stepson. She and Antony failed in the battle at Actium. They both committed suicide. When she died, the Ptolemaic dynasty ended. Rome took control of the Grecian kingdom.
Verse 18: he = Julius Caesar again for emphasis. War in other parts of the empire drew him away from Egypt. He invaded all the remaining coastlands of Africa, Syria, and Asia Minor.
Rome was a republic. After many successful conquests, Caesar's arrogance caused his assassination. Caesar wanted to remove the Republican form of Government and become Dictator. Out of fear, those that were "with him" in this desire also feared death and so turned on Caesar. Hence the famous final statement of Caesar, "et tu Brute" which translated means "and you, Brutus?"
Verse 19 tells of Julius Caesar returning to Rome where he is stabbed 23 times by Cassius, Brutus and others. His assassination happens in the Theatre of Pompey in Rome on the ides of March (March 15), 44 BC.