Where the decan sits
Each sign holds three decans of ten degrees. This is the last of Gemini's, running from twenty degrees up to but not including thirty, at which point the Sun enters Cancer at the June solstice.
The Sun spends roughly ten days here, from about 11 June to about 21 June. Those dates are a guide rather than a rule. Because the calendar year and the tropical year do not match exactly, the ingress into Cancer moves, and with it the start of this decan. A day and a half of drift either way is normal, which matters most for anyone born in the days right at the end.
Aquarius in one scheme, the Sun in the other
Under the triplicity method the decans of an air sign go to Gemini, Libra and Aquarius in that order, so the third decan of Gemini falls to Aquarius. In modern practice Aquarius is given to Uranus, though older texts kept it with Saturn.
The Chaldean order takes no notice of element. It cycles Mars, Sun, Venus, Mercury, Moon, Saturn, Jupiter from the start of Aries, and the ninth decan in that count comes out as the Sun.
So the answer is Uranus or the Sun depending on the method, and articles quoting one of them rarely say which. That is worth knowing before you read too much into a single source.
What each layer is taken to contribute
Gemini shaded by Aquarius is read as curiosity pushed outward from the personal to the general. Gemini on its own is described as quick, plural and interested in the next thing; the Aquarian overlay is taken to give that restlessness a subject, usually systems, groups or ideas held at some distance from the speaker. The tradition reads it as the part of Gemini most likely to argue a position rather than simply relay information.
The Chaldean Sun is taken to add something the sign does not supply on its own, which is a centre. Where Gemini scatters, the Sun is read as a fixed reference point, an interest that persists under the variety. Read together, the pairing is described as someone who covers a lot of ground but keeps returning to one question.
Set the confidence appropriately. Decans come down to us from Egyptian star lists used to mark the hours of the night, and they are a real strand of the tradition, but they refine a reading rather than carry it.
It is also worth noting what the modern ruler does to the reading. If you keep Aquarius with Saturn, as pre-modern texts do, the description turns towards structure and formality instead of the disruption Uranus tends to bring with it. Which of those you prefer is a choice about how much modern rulership you accept, and it changes this decan's portrait more than most.
Other placements, and the boundary problem
Decans are not a Sun technique in origin. Any point in a chart falls in one, and the Ascendant and the Moon are read by decan routinely. If your rising degree lands in the last ten degrees of Gemini, the same material applies to it.
Because this decan ends at a solstice ingress, the closing days are the ones most often misread. The check above works out your solar degree directly from your birth date, so a birthday on 20 or 21 June gets a definite answer instead of a range that may or may not include you.
Questions people ask about this
What dates are the third decan of Gemini?
Roughly 11 to 21 June. The end of the decan is the moment the Sun enters Cancer, which shifts between years, so late birthdays should be checked rather than assumed.
Who rules the third decan of Gemini?
The triplicity scheme gives it to Aquarius, and so to Uranus in modern practice or Saturn in older texts. The Chaldean order gives it to the Sun. Both answers are in circulation.
Why does my decan ruler differ from what I read elsewhere?
Almost always because the other source used a different scheme and did not name it. The triplicity answer and the Chaldean answer for this decan are unrelated planets, so the readings diverge sharply.
What does Aquarius add to Gemini?
The tradition reads it as a widening of scope, from personal exchange to systems and groups. It is described as the most opinionated stretch of an otherwise flexible sign. That is interpretation, not measurement.
Can I use decans for my Moon or Ascendant?
Yes. The technique applies to any placement, and the Ascendant is a particularly good fit because it is calculated from your birth time to the minute.
How old is the decan system?
The division of the sky into thirty six parts comes from Egyptian star lists used to tell the time at night, well before it was attached to the zodiac signs. The rulership schemes layered onto it are later.