Select the appropriate preposition to fill in the blank in the following…

English prepositions of time follow a fixed distinction by the span of time they cover: "at" marks a precise point in time (a clock hour, noon, midnight), "on" marks a particular day or date (including named calendar occasions), and "in" marks a longer enclosed period (a month, a year, a season, a century).

1. The word following the blank is "birthday", which names one specific calendar day, not an extended period or a single clock moment.

2. Since the noun is a specific day, the day/date rule applies, and the temporal preposition that pairs with a specific day is "on" (compare: on Monday, on Christmas Day, on my birthday).

3. "In" is eliminated because it pairs with months, years, or seasons, not a single day.

4. "At" is eliminated because it pairs with a precise clock time or moment, not a full calendar day.

5. "Into" is eliminated because it is a directional preposition of movement, not a temporal preposition, so it cannot fill a time blank at all.

This matches the same pattern used in other well-known day-linked constructions such as "on Sundays" and "on New Year's Day", confirming "on" as the consistent, non-exceptional choice.

Therefore, the correct preposition is "on".