I would like to get my ArcGIS Server Feature Service details including running or stops services details using Arcpy.
Kindly request to suggest me.
Arcpy doesn't have any functions for this type of thing. You'll want to use the json and urllib2 modules:
Scripting with ArcGIS REST API—ArcGIS Server Administration (Windows) | ArcGIS Enterprise
ListMapServices—Help | ArcGIS Desktop
Retrieving data ...