Have your Gallery Admin check under your Subscription details to see if the API is enabled. There is a yes/no selection there that must be on in order to use the API
@pushpraj From the images you have shared, in your local environment, you are looking for POST API in Admin section of the API docs page. however in Alteryx Public Gallery, you can see the POST API in Subscription section of the API page.
You can either remove admin from your gallery URL or you can click on Subscription section in the API Docs page. Pleas refer to attached screenshot of Subscription section.