Years are measured based on factols’ rules.
In the Cage: A Guide to Sigil, p.12, “Time and Direction in Sigil”, describes how time is measured.
The Cage is eternal, so much so that no one knows the date of its creation or founding. The Lady surely was present, but whether she and Sigil came into being simultaneously or she preceded the city will never be revealed. Years are measured, then, from beginnings of factols’ rules, most often according to those of the Fraternity of Order. (The current date is the 127th year of Factol Haskar’s reign.) Clueless visitors often are confused by this timekeeping system, but those who stay long enough soon realize that with the constant changes in Sigil it doesn’t matter too much precisely how long ago something happened.
Time is also described here as measured in terms of “peak” (noon) and “antipeak” (midnight), with all other times measured in number of hours before peak (B.P.) or after peak (A.P.). Times are also measured in hours before and after antipeak, and all clocks are 24-hour. Days, therefore, work similarly to how we would expect.
There are numerous references in this book to months and weeks. The week, at least, seems to be strictly defined for the purposes of commerce; e.g. usury laws set a maximum rate of interest on loans to 25% per week. In the Cage doesn’t define the length of a week or month, although according to page 67, officers of the Hall of Offices work five days a week, so there must be at least five, and it would not be an unreasonable guess that their work week is five out of seven days like our own.
The length of a month is not defined in this book, but there are references to organizations charging monthly fees, which implies a standardized calendar of months. There are no names specified to the months, and we don’t know if they’re regular (like World of Greyhawk) or irregular (like real-world months).
The calendar system described on the Sigil: City of Doors Wiki appears to be entirely homebrew. I can’t find any reference to a 13-month calendar or the named days given in that article. However, the calendar of thirteen 28-day months in a year is convenient as it creates a regular 364-day year, which matches up with the calendar of World of Greyhawk.