For example, how do you say:
It's quarter to 3.
and
It's quarter past 3.
For example, how do you say:
It's quarter to 3.
and
It's quarter past 3.
A quarter to three is 2時45分 (にじよんじゅうごふん), and a quarter past three is 3時15分 (さんじじゅうごふん).
If we want to emphasize the difference from three o’clock, we can say “3時の15分前” and “3時の15分後,” but this is not the usual way to state the time.
In Japanese, there is probably no simple expression for a quarter hour. You have to say 3時15分前 or 3時15分.
For a quarter century or quarter period, there are expressions 四半世紀, 四半期.