Here is the example how you can stop/serve your App Engine version using API, just replace the PROJECTID,SERVICEID and VERSIONID:
 curl --request PATCH \ "https://appengine.googleapis.com/v1/apps/PROJECTID/services/SERVICEID/versions/VERSIONID?updateMask=servingStatus" \ --header "Authorization: Bearer $(gcloud auth print-access-token)" \ --header "Accept: application/json" \ --header "Content-Type: application/json" \ --data '{"servingStatus":"STOPPED"}' \ --compressed 
 For you to fully understand how it builds, there's an API Explorer or a panel. It has a title "Try this API" in the right side of screen, click the box icon to maximize or click this link to redirect. Fill the required fields:
  - appsId- your PROJECT ID.
- servicesId- go to App Engine > Services or execute- gcloudcommand:- gcloud app services listto see your App Engine Services. The default name or- servicesIDof your App Engine Services is default.
- versionsId- go to App Engine > Versions or execute- gcloudcommand:- gcloud app versions listto see the App Engine versions deployed and copy the VERSION ID you want to update.
- updateMask- the configuration in App Engine version you want to update, example: servingStatus or instanceClass
To know more about fields and its definition in API, visit this table of contents. It will help you a lot how you can configure your App Engine Versions via API.
  NOTE : You cannot stop the App Engine Version if your apps is configured in automatic scaling.