Is this part of the fascia or soffit?

Neither fascia or soffit
They are either structural (maybe the first … to support the wide roof overhang )
Or decorative (definitely the second … May have been installed to balance the look cuz of the first )

* Facia = Facing front edge
* Soffit = Facing underside

In your pics facia appears brownish
And soffit appears light cream / white

It's definitely bizarro, especially that brick column.
I sometimes why architects do this kind of stuff. I've seen too many complicated roof designs that only lead to water infiltration issues, especially in multiple freeze/thaw winters.
I'm not a fan of Mike Holmes, but he had an amusing episode where a false dormer was added to roof for a 'look'. It was causing leakage because it wasn't flashed properly, but the funny part was him going off about why it looked stupid in the first place.

Many 5 level backsplit homes in my area have this design under the gable. The house is 35 years old.