The Tropic of Cancer is the the closest part of the globe to the sun on June 21st. If you live North of 23.5 degrees then June 21st is the longest day of the year (most daylight anyway). If you live at 20N when is the longest day of the year? There should be 2. Please show me where to find the answer.
Any location on Earth (excepting points along the equator where the length of the day is the same all year) only has one longest day of the year, which is the summer solstice.
The only thing that’s special about the Tropic of Cancer is that the Sun will be directly overhead at noon on the summer solstice. South of the Tropic of Cancer, the Sun will be in the northern sky at noon, but the solstice will still be the longest day of the year.
The US Naval Observatory will give you a year’s worth of sunrise and sunset times for any point on the Earth. If you want to, you can do some subtraction to find the length of the day.
Why would the day get shorter after the Sun moves farther north than your location? I don’t know why you assume there would be two longest days.
There will however be two days in which the Sun is directly overhead, as opposed to one on the Tropic.