This is an accepted solution.
welcome to shopify community.
To create a private app you can follow some tuturials on youtube or from some articles.
I can guide you how you can do that in PHP
You need to have a partner account
then create app and put https url and redirect URL
URL will be where store owner will be redirected first time and then after confirmation they will be redirect to redirect URI
Then you need to grab info and create token, there are different methods for that and a lot of code available online