What time is 0338 in military time?

0338 (or 03:38) is 3:38 AM.

The other way round: 3:38 AM in military time is 0338, said “zero three thirty-eight hours.”

Military time	0338 hours
24-hour clock	03:38
12-hour clock	3:38 AM
Said out loud	“zero three thirty-eight hours”
Minutes after midnight	218
Share of the day gone	15.1%

How to convert 0338

The hour is 03, which is before 12, so it's a morning time: drop the leading zero, keep the minutes (38) and add AM. That gives 3:38 AM.