Verified answer

As a general rule and in almost all cases, ず is used.

One important exception to this rule is as follows:

In the second half of a two-part compound word, the original つ is changed to づ。　For example:

気付く　= 気（き）　＋　付く（つく）　→　きづく

Not きずく because the original second word is つく、not すく

折鶴　＝　折（おり）　＋　鶴（つる）　→　おりづる

Not おりずる because the original second word is つる、not　する

小遣い　＝　小（こ）　＋　遣い（つかい）　→　こづかい

Not こずかい because the original second word is つかい、not すかい

小津　＝　小（お）　＋　津（つ）　→　おづ

Not おず　because the original second word is つ、not す

.

I guess there're only some cases that you're supposed to write づ instead of ず while you pronounce them the same way.

Offhand, there are only two cases which occur to me when to choose to write づ.

#1: The family name 小津（おづ）

Use づ to write the family name 小津（おづ）not ず.

#2: The phrase 少しずつ（すこしずつ）

Write 少しずつ not 少しづつ. (Even some Japanese people mix them up.)

For your record, some people, as a joke, write ～ぢゃない not ～じゃない. (じゃない is a correct way to write.)

I hope it'll help.