Both are possible, but if you put it after the word, it sounds more formal and official. Kind of like English "my mother" vs. "mother of mine". For example:
- When Her Grace says "Valyrian is my mother tongue", she says Valyrio muño ēngos ñuhys issa, "Valyrian mother tongue of-mine is" (S03, E04).
- But when trying to calm down a citizen, she in her wisdom chooses the more casual pattern, with "my" first: "Zūgagon daor, ñuhys raqiros. "Fear not, my friend" (S04, E10).