The wheels from https://www.lfd.uci.edu/~gohlke/pythonlibs/ are not created by the Fiona project and thus we can no support them here.

In general, the install instructions from this site should be followed.  E.g. regarding Visual C++ Redistributable, package dependencies etc. If e.g., it says that a package requires a dependency, this dependency should be installed before. With gohlke's wheels, both the rasterio and fiona packages require the gdal package (this is not the case for the wheels provided by the Fiona project over pypi). Make sure that the packages are installed simultaneously. E.g. if fiona should be updated, it is very likely that also the gdal package must be updated beforehand (respectively all other packages that depend on the gdal package).