A green archipelago OF the northern tip of modern Scotland - doesn't really mean anything. It is not idiomatic. Or it could mean it is attached to the mainland. Which obviously - it isn't as it's... an island!
A green Archipelago OFF the northern tip of modern Scotland - correctly refers to the island being related to the northern tip of Scotland but some distance away.
Your 'solution' is not grammatical, by the way - maybe that's a typo or three - if it read like this, it might make more sense:
- "the preposition 'of', before 'northern tip' - has been used incorrectly." (I think it's preposition here, not proposition!)
...Meaning - you need OFF with two f's - not OF, as the meaning is quite different.
When an island is 'off' something - it means 'somehow related - but some distance away' from it.
Other things can also be referred to as being 'off' something, for example:
- the Globe Theatre lies off the main street
- The market is off the main playing field
- the living room lies off the dining room.