any help given with the following problem would be highly appreciated:

which of the four phrases would be correct?

1) "king arthur of britain's sword"
2) "king arthur's sword of britain"
3) "king arthur's of britain sword"
4) "the sword of king arthur of britain"

i'd go for 1) and 4). reasons: 2) changes the meaning (the sword has the britannic attribute, no longer the king) and 3) separates the genitive construction.
i'd learned in school that the "of" genitive is seldom used with persons as referrers. but as far as i can remember, it is used if "'s"-construction is impossible, which, to my mind, would be the case especially if "king a of b" could not be seen as a clear single entity.

is this, or probably rather any of this, correct?

thank you very much in advance,

All the phrases need proper capitalization.
The choice between #1 and #4 depends on the context.
For example, in a museum display of the object, I would choose #4.
Hi, and thanks a lot for the answer!

Sorry for the missing capitalization, my usual laziness on the Internet had taken its toll...

Could you please elaborate a bit on where you would use no.1? And would you have a different opinion on the construction if the phrase was, e.g. "Queen Jane of India's book / the book of Queen Jane of India" (i.e. if person and apposition are not as well-known and thus appear as a unit so obviously)?

Thanks again in advance,