First, Figure out where is the 'global' setting is taken from -
C:> pip -v config list
It will print something like - For variant 'global', will try loading 'C:\ProgramData\pip\pip.ini' ...
Create the file if does not exist (C:\ProgramData\pip\pip.ini) and edit it with the details of the private pypi, for example -
[global]
trusted-host = repo.myprivaterepo.io
index-url = https://repo.myprivaterepo.io/repository/pipall/simple/
index = https://repo.myprivaterepo.io/repository/pipall/simple/
Should work now...
Go through any of the other files from the pip config output, and remove the contect of them.
Good luck! commend for any questions