In English, a person can be described as standing in the middle of the sidewalk in the middle of the day, and whether you are talking about place or time, the phrase "in the middle of" is correct. In German, however, there are two expressions: mitten im (or mitten in der for feminine nouns) and mitten am (mitten an der for feminine nouns). In most cases, whether discussing time or place, the phrase mitten im (in der) is used, whether for time of the year:
Vor langer Zeit mitten im eisigsten Winter...
A long time ago in the middle of the iciest winter...
Caption 5, Märchen - Sagenhaft - SchneewittchenPlay Caption
Or for place:
Ich finde das eine, ja, auch wichtige Stelle, mitten in der Stadt.
I think it is also a, yes, important place, in the middle of the city.
Captions 25-26, Holocaust-Gedenktag - Gedenkstätte am MichelsbergPlay Caption
The phrase mitten am (mitten an der) is used less frequently but in very specific contexts. For place, mitten am is used primarily when something is physically located on a place. In the following example, you can see why mitten im would sound wrong, as it would suggest that the kiosk is inside Friedberger Platz rather than on it:
Neben mir steht der Turan,
Next to me stands Turan,
der Besitzer hier von dem schönen Kiosk mitten am Friedberger Platz.
the owner here of the nice kiosk in the middle of Friedberger Platz.
Captions 1-2, Frankfurt - Der Friedberger PlatzPlay Caption
Generally you wouldn't say mitten am Friedberger Platz anyway, you would simply say auf Friedberger Platz. If the kiosk were located on the edge of the square, you would say an Friedberger Platz.
When used with period of day terms, it is more common to use mitten am than mitten im: Mitten am Morgen (in the middle of the morning); Mitten am Nachmittag (in the middle of the afternoon); or Mitten am Tag (in the middle of the day, or "in broad daylight"). When discussing nighttime, however, the mitten in der phrase is standardly used: Mitten in der Nacht (in the middle of the night). In general, mitten does not have any influence on the above usage of the prepositions am or in der, as they are also am Morgen and in der Nacht etc. when used without the word mitten.
Look for further examples of mitten im, mitten in der, mitten am, and mitten an der on Yabla German to see these phrases used in a real-world context.