To express possession you normally say
Das gehört mir.
Das ist meins.
But there are regions where people regularly say
Das ist mir.
Which are these regions and is there are terminus technicus for this dialectic form?
I don't know whether "possessive dative" is a current grammar term, but one might called the thing in this way. "Das ist mir" - I would consider this use as regional and substandard, but I don't know in which regions this expression is used. But "Das ist doch dem Paul sein Fahrrad" is colloquial language. I even remember the title of an older dictionary: Dem deutschen Volk sein Wörterbuch.
I just see that Die Grammatik (Duden, 8th edition) also has the term "possessive dative". In the register: Dativ, possessiv. In paragraph 1275 Duden says that possessive dative has been known in the whole of the German speaking area for a long time, but it is not standard language ( Duden should add "in written language").
I'm from Hesse(n) and I use "Das ist mir" all the time, even when I try not to.
Fun fact, I didn't know this wasn't standard German until I started university. I just thought it was colloquial. I wouldn't have written it down in an essay, but I thought it was used that way everywhere in Germany. Oops.
But "das ist meins" und "das gehört mir" still sound very stilted to me.