Please help me authentify this watch ;)

JimInOz

29mm would make it a 13''' (28.9mm) size. I can't find a 13''' with that configuration.
Did you exclude the casing ring from your measurement?
The closest example I can find to that configuration is a 12''' (26.5mm).

This caliber was introduced in 1899 and was used in Omega's first wrist watch. It had technical problems and was withdrawn in 1923.

So, the outcome is that an enterpising watchmaker went through their parts drawers and found enough bits to make a watch.

JimInOz

Omega often marked early serial number on the plate under the dial, except when they didn't and marked them on the bridge.
Omega has been known for such inconsistencies.