The minor version matters, it must be 3.**6**. The patch version usually does not (3.6.**N**), but QGIS.org specifies 3.6.5 as a minimum.  

You can not use Python 3.7 or non-python.org distributions (note: some people have reported mucking around with symlinks to mimic a standard python.org 3.6 install path to get python 3.6 from homebrew/anaconda working).

From the [download instructions on QGIS.org][1]:
> This package uses the python.org Python 3.6, at least version 3.6.5, the "macosx10.9" build - other distributions are not supported.


  [1]: https://qgis.org/en/site/forusers/download.html#mac