Use 'in + [period of time]' to refer to an unspecified point in that period of time:
- a month: Susan's birthday is in December. [= Her birthday may be December 1st, 3rd, 10th, 25th, 31st, etc.]
- a year: She was born in 1969. [= Her birthday may be Jan 25th, February 13th, April 6th, October 21st, etc.]
- a season: She was born in the fall.
- a part of the day: She was born in the morning.
Unlike 'in', the preposition 'on' refers to specific days:
- days of the week: She was born on Saturday.
- specific dates: She was born on December 21st.
We put our finger on a specific day of the calendar:
"My birthday is on the 21st."
Use the preposition 'at' to talk about a specific time.
- She was born at 5 o'clock in the morning.
- She was born at midnight/noon.
- She was born at night.
Note that we say 'in the morning/afternoon/evening' but 'at night'.