"In the north of"
The word fy which means "my" does cause nasal mutation, but it turns words beginning with c into words beginning with ngh (e.g. fy nghar for "my car"); ng without a following h comes from g, as in fy ngeni "my being born").
The word yn, when it is a preposition meaning "in", also causes nasal mutation -- so for example, Cymru "Wales" turns into yng Nghymru "in Wales" with ngh- instead of c-, and gogledd "north" turns into yng ngogledd with ng- instead of g-.
(And when yn comes before a word starting with ng-, including ngh-, it turns into yng itself; and when it comes before a word starting with m- or mh-, it turns into ym, as in ym mis "in the month of ..." or ym Mangor "in Bangor".)
What I'm less sure about is the yn y gogledd. I think that's fine for "in the north" by itself, but if you want to talk about "in the north of X", I think you would just say yng ngogledd X, since gogledd in the compound gogledd X is definite from the construction already - gogledd X is "the north of X" and you can't add an extra y to it.