I have a 1967 coupe barracuda with a low serial number and shipped march 1966.

16richard said
If you have fast backs , coupes and convertibles starting a new model how would the serial numbers start . I may be wrong but 01001
could be for the first convertible 02001 for the first coupe and 03001 for the first fastback ???

No.

It did not work that way.

Photos of what you actually have may help here?