Maseches Shekalim is the fourth Masechta in Seder Moed. While it opens up with the fact that the Beis HaMikdash treasurers would collect the Shekalim every Adar, the rest of the Masechta talks about what they did with the Shekalim, various vessels and positions in the Beis HaMikdash, and certain relevant halachos of Karbanos. Shouldn’t this Masechta be in Seder Kodshim? Why is the opening Mishnah, the one fact that they collected in Adar, so important that it lands the Masechta a spot in Moed, when most of the Masechta has nothing to do with any particular time of the year?
The Meiri answers your question in his introduction to Berachot (as quoted in artscroll's introduction to Shekalim):
Logically, the subject matter of this tractate would seem to belong in Seder Kodashim, which discusses the procedures of the Temple. Since, however, the half-shekel was collected at a fixed time each year, so as to conform with the requirements to "renew" the Temple service annually, its laws were arranged in Seder Moed, which deals with the commandments that are linked to the calendar. [...] Another connection between Shekalim and the festivals is that the half-shekel levy funded the special offerings that were brought on each festival.
R Sherira Gaon adds
And since the time allotted for the giving of the shekel - the month of Adar - closely precedes the festival of Pesach, this tractate was juxtaposed to Pesachim.
This is from the opening paragraph to R' Adin Steinsaltz's introduction to Shekalim that appears in the Koren Talmud Bavli (the rest of the intro can be found here):
Tractate Shekalim deals primarily with the finances and organization of the Temple. Based solely on content, this tractate rightly belongs in the order of Kodashim, the fifth order of the Talmud, which deals with matters pertaining to offerings and the Temple service. Nevertheless, Shekalim was placed in Seder Mo’ed, the order dealing with the Festivals. This presumably had to do with the fact that the shekels were collected at a fixed time of the year, and the collection of the shekels would precede, and sometimes even determine, the dates for various aspects of the Temple service and related events.
Because the fixed time of the year has ramifications to the development of the following calendar year it was placed in the seder. Unfortunately, there is no source provided