Ok, what is on you are reading is not "Girl of mine" or "This girl belongs to me", the word esti is an old latan word that means "to be", so you should acctually read it as "This girl is to be mine", meaning that whatever it is that is terrorizing you, is trying to claim you, but does not yet have control over you.
This was acctually a very common saying use in Salem, 200 years ago, when witches would curse families of important figures when they intended to take their children.
But it originated long before that, durring the middles ages, by kings, lords, etc. etc., who would take random children to be servents.
This is a term I acctually come across quite often, and is commonly misinterprited.