I recently saw a unusual BMW parked in the back of a body shop.It has single retangular plastic lens headlamps on each side. It looks like a 3-series from the eighties. The only marking on the car is a " turbo " script on the trunk. The car doesn't look like it was modified in any way . Could it be a European model ? I may be making the owner an offer if the car is of some value .
Unless you were off by a decade and it was a 2002 (Don't recall tho if they actually badged them turbo or not), then that would be just someone's 'made' badge they decided to attach to the car. Hopefully, they remembered to attach a turbo with the badge.
Possibly some BMW tuner company made a limited run of cars, but most BMW bred tuners don't slap turbo/SC's on them, they put bigger NA engines in them. (Alpina leaps to mind)
Until the new Bi-Turbo 335i 3 series that was just , BMW did NA-only production engines since the last turbo job - the 2002 from the early/mid 70's.