Na

South Eastern dialect of Serbian has a peculiar grammatical construct. It uses "na" meaning "on" to express belonging, possession. This construct using the word "na" exists (as far as I know) also in neighboring Macedonian and some Bulgarian dialects, all centered around southern Carpathian or Balkan mountains.

South Serbian:

Q: Na koga je ovo kuče - on whom is this hound (whose hound is this)? 

A: To je kuče na Petar - this is the hound on Petar (of Peter)

Bulgarian:

A: Tova e kuče na Petar - this is the hound on Petar  (of Peter)

Macedonian:

A: Toa e kuče na Petar - this is the hound on Petar  (of Peter)

This construct defines possession through physical contact which is the oldest known form of possession. What belongs to me is on me, within my boundary, within what i can grab, hold, wear, carry, protect...

Fernand Cormon, Cain, Musée d’Orsay, Paris

What is interesting is that the Irish language has the same construct. On the page about Hiberno-English (English dialect spoken in Ireland which is hugely influenced by the Irish grammar and vocabulary) we read:

There are some language forms in Hiberno-English that stem from the fact that there is no verb "to have" in Irish. Instead, possession is indicated in Irish by using the preposition at, (in Irish, ag.). To be more precise, Irish uses a prepositional pronoun that combines ag "at" and mé "me" to create agam which basically means "at me, on me". This is then reflected in Hiberno-English, where the verb "to have" is used, interchangeably with phrases "with me" or "on me" that derive from "tá … agam". This gives rise to the frequent:

"Do you have the book?" – "I have it with me."
"Have you change for the bus on you?"
"He will not shut up if he has drink taken."

My favorite Irish Gaelic expression using this construct is "Tá áthas orm" meaning "I am happy, I have happiness" but literally meaning "There is happiness on me" :)

So what language did this construct originate in: Irish or these south Slavic dialects? Remember that the Irish language only has this constrict to express possession. And that this part of the Balkans was once "Celtic central" and is the area where we still find "Celtic" village crosses, like this one from Crna Trava:

And how old is this construct? Is it possible that this is a true linguistic fossil, which comes to us from the time before settled communities and static property? 

And does a similar construct exists in any other language? 

Well it seems that it does. In Finnish of all languages. Finnish doesn't have a separate verb for "to have". Instead it uses a different sentence construction, centered around the verb "olla", "to be". It's interesting to note that the "minulla on" literally means"on me there is". 

Very interesting, because it shows the age of this construct.