Any Shopify store can access Shopify’s Application Programming Interface (API) through its own store-generated login. There may be times when you need to provide this Private Shopify API login to developers or third parties. The private API key is different from using the Shopify app, so make sure this is the type of access you’re requesting. This article will show you how to generate an API private key
Step By Step
Step 1: Go to admin section in Shopify, click on Apps, then Manage private app

Step 2: Fill the private app details form

Bellow are some instructions for creating api private key with shopify. Hope you enjoy it!