it's Saturday morning

it's Saturday morning这里表示时间是周六上午.

it's on Saturday morning表示某事发生在周六上午.

如果用ON的话
就要省略掉前面的IT IS

口语表达方式一般比较简便。
若要说on Saturday morning, 前面最好有一定的情景描述，比如
She arrived on Saturday morning.