For example, I would like to get how many request I have done in the last day or month. I'm using YouTube Data API v3. I know that we can see the request count on this page : https://console.developers.google.com/apis/dashboard
There is currently no way to retrieve this using the API. Only the dashboard tool, which you are aware of, lets you keep track of your quota usage. The closest thing from the docs is a Quota Calculator which lets you estimate how you use quota.