I entered Sweden July 17 from the US. My 90 days were up on Oct. 14 however I applied for a tourist extension to extend 30 more days. I never got a response and the consulate told me I was okay to stay in the country until I got a response (even though I was there longer than 30 extra days). I ended up leaving Nov. 20. The 180 days from July 17 would be Jan.12 2019. I stayed 120+ days of the 180 legally. Does a new clock rest on Jan.12? I would like to re-enter Schengen country on Jan.13
There is no "resetting", and the particular 180-day period that happened to start on the day you first entered has no special significance.
The rule is: On any given day you can only use the "short visit" rules if you have been inside the Schengen area on at most 90 of the last 180 days.
If you were to attempt to enter on January 27, for example, the relevant question would be:
how many days have you been in the Schengen area (other than as authorized by a long-stay visa or residence permit) in the 180 days from August 1 to January 27?
The answer is "112 days already", and if you were allowed to enter on January 27, it would become 113, which is more than 90. So you cannot enter as a "short visit" on January 27.
After a continuous stay of 90 days or more, what this works out to is that you need to be outside the area for 90 entire days before the "number of days inside in the last 180 days" has become small enough that you can enter again. If you left on November 20, the earliest you can enter will be February 19.
As already answered there is no reset on new year or something like that. However not all days that you spent in schengen count for the calculations of the schengen visa. I do not know what exactly a tourist extension is but it may not count in your calculations.
I know this because In the case of a friend she had been in Germany on a student visa and when it ran out she didn't have her permanent visa yet and would have been more than 90 of the last 180 days in Germany (160). So she inquired and it turns out that only the days that you were in schengen using the schengen Visum count, so she had 0 of the last 180 days used.