It is a 509, or more likely the improved 509A engine, done after 1925. It should have a Fiat sign at the other side of the block with a serial number and "Tipo 109A" printed to it. Atleast my 509A engine says 109A, not 509, as according to Centro Storico archives the number one refers to the serials of the engine factory. Similarly, for example, 501 parts are often tagged with the code Tipo 101. Also the starter, gearbox, dynamo and possibly the steering box all have similar numbers casted or stamped in the casings.
I have sadly been told, that the factory museum can identify vintage Fiats only by their chassis numbers, as records were kept only for those before 1980s. With the chassis number they will gladly check the production month and the body type (or bare chassis) of your car.
Take care of your gem, it is a rather rare find with all the auxilaries, you only miss the horn in front of the engine. The carburator should be a quite common Solex 26 or a finer Memini for sports models. The electrics are 12V and the whole car was very modern in many aspects, I like to think that how it only had 990cm3 and still could give as much power as a Ford Model A. Also, the castings are very beautifully done in 509.
Ps. there are time to time some head gasgets made by Payen for sale for 509 in subito.it and ebay, I bought one with a nice price but our local mailman stuffed the parcel to our mailbox so I now have a new but damaged template of a head gasget.
Its not on the LH chassis rail where i was told by FIAT?