Actually i want to execute a functionality every time a developer publishes customizations. Hence, can we write any custom logic on click of "Publish entity" or "Publish All Customizations" buttons. OOB or un supported way either?
Its not a business requirement, its more of a streamlining code development process in the team.
This is an example which explains how to create a plugin for the Publish/PublishAll events. I created it for a very similar question so I'm sure that you will find it helpful.
You can download the plugin project and CRM solution that I used for that example from my GitHub.