Fossil Neutra Chronograph - Tyler Hoechlin - Superman & Lois
The Fossil watch is only worn when the Kal-El character is in his Clark Kent outfit, not when he wears his Superman suit.
There are a few variations of this particular Fossil watch, but I'm fairly sure that he wears the Fossil Neutra Chronograph Brown Leather Strap FS5453. The dial of the FS5453 watch looks blue in the product photos, but in real life is just as dark (almost black or dark grey) as in the screenshots from the tv series.
Other similar variations are the FS5512 (dark grey dial, but it has a matte, darker case and darker brown strap), FS5408 (grey case, but it has a gold color crown) and the FS5708 (blue dial, comes in a set with a bracelet, this watch is probably very similar to the FS5453).
Complete the look
Clark Kent wears Ray-Ban Clubmaster Square eyeglasses in the same outfit, read more on SunglassesID.com.