Euro made. Get an appraisal
It won't have one. There may be some numbers under the barrel on the forearm, but they will not be serial numbers.
Check under the forearm
Serial numbers were not required before 1968. If it has one, check under the forearm, on the barrel and on the action.
Watertable, forearm metal, and barrels
Take the forearm off, it's usually on the bottom of the barrels.
Check the top of the receiver and under the forearm.
Before they were required to be clearly visible on the receiver, one may have been on the lower tang (behind the trigger) or under the forearm, either on the forearm or the bottom of the barrel. Since these guns were made many years before serial numbers were required, there may not be one.
Forearm iron and watertable are the easiest places to obtain this info
My brother has the same type shotgun. He says to look under the forearm of the gun and the serial number should be there. The forearm being the part that would be held in the left hand if a right handed person was aiming the gun.
If it is a Side by Side like my Western Long Range Gun, pop off the forearm - mine is marked in three places: the wood of the forearm, the metal of the forearm, and on the action. My Model 37 has the serial number stamped on the front of the reciever, opposite the slide for the pump. It is in the area between the magazine tube and the barrell.
There is no serial number on your shotgun. Serial numbers were not required befroe 1968.
That depends on the manufacturer. Different brands can have different lengths of serial numbers.