I'm the king of the castle

Origin of "I'm the king of the castle, and you're the dirty rascal", pls?

English boys (childrens) game, at least back to 1850's. "King of the Hill" etc.

Games and sports for young boysý - Page 4
by Games - 1859 - 80 pages

KING OF THE CASTLE. One player gets on the top of a little hillock or mound of dirt, etc.
... couplet : - " I'm the King of the Castle, Get down you dirty rascal

Also known as "King O' The castle", Scotland, your version is called London version by some,
in North America by 1870's.

It goes back much further than that. There's a near-contemporary account of the siege of Hume Castle in the English/Scottish Civil War in which the Roundhead commander Colonel Fenwick demanded the surrender of the castle, and the governor, Thomas Cockburn, replied to him thus:
"I William of the Wastle
Am now in my Castle,
And awe the Dogs in the Town
Shan't gar me gang down."
- whereupon "Col. Fenwick having placed a battery against the Castle, returns him Heroick Verse for his Resolute Rhymes".

There's no suggestion that Cockburn invented this bit of doggerel; he was obviously using a well-known children's rhyme, which indeed may already have been anything up to a millennium old. There are French and German equivalents, and in 20 BC the poet Horace wrote down the Latin verse that Roman children used for the same game:
Rex erit qui recte faciet;
Qui non faciet, non erit.
(VSD)