Title pretty much says it all. I've seen these:
How to trigger Multibranch Pipeline build with github webhook
https://support.cloudbees.com/hc/en-us/articles/224543927-GitHub-webhook-configuration
https://support.cloudbees.com/hc/en-us/articles/115003019232-GitHub-Webhook-Pipeline-Multibranch
I have a github server setup in jenkins, but cannot choose it in the multibranch source (as one of the links suggests), it asks for credentials but no credentials are in the dropdown.
I've also setup a github webhook, but I dont think it makes any difference
So, you need just add(create) this credentials in order to be able choose them in dropdown. It could be API key or SSH key. One of your links includes the manual how generate API key:
You can find more information on the GitHub token permissions here: https://support.cloudbees.com/hc/en-us/articles/234710368-GitHub-User-Scopes-and-Organization-Permission
I hope it will help you.
I needed to create credentials with username equals to username and password equals to the github token