Ran across an Omega trench watch and can't find any info to authenticate it. Here is info. OMEGA WATCH CO. SWISS; 7 Jewels; Adjusted 2 positions; 4910214. Watch is in Star Watch Co. case serial number 3703289 and is warranted 20yrs.

Trench style or tank style wristwatches from the first world war were typically private purchases by soldiers and civilians who wanted to be stylish. Since you have not indicated that yours has military markings I would assume that it is one of these private purchase wristwatches.