my laptop model is hp pavillion au623tx 8 gb ram,4 gb nvidia 970 mx.
Laptops made in about the last 5 years with Nvidia GPUs use something called Optimus to swtich between the Intel and Nvidia GPU. The Intel GPU always drives the screen, the Nvidia GPU acts as a co-processor and sends completed frames to the Intel GPU for display.
1) Make sure you have the Intel and Nvidia drivers from your laptop vendor's support page installed. Downloading the drivers directly from Intel and/or Nvidia will break Optimus. If this computer was upgraded from an older version of Windows to Windows 10, Win10's auto-update might have broken Optimus. (In which case you'll have to disable the Windows Update service, and install the proper graphics drivers from your laptop vendor's support page. About once a month you'll have to re-enable Windows Update to get new security updates, then disable it again and reinstall the proper graphics drivers.)
2) Right-click your desktop and open the Nvidia control panel. Go to "Manage 3D settings." From there you can whether each game should use the Intel or Nvidia GPU, as well as default behavior.
Some older games do not work with Optimus. They were coded when computers only had a single GPU, and stop searching for a GPU after they find one. Since the Intel GPU always drives the screen in Optimus laptops, that first GPU is the Intel. And these games are unable to use the Nvidia GPU at all.
As for playing on battery, the 970m is a very power-hungry GPU (about 75 Watts - that's what my laptop has as well). Your battery probably cannot put out enough current to drive it at full power, so the laptop has to throttle it and/or the CPU when you play games on battery. So your framerate on battery will never be as good as when plugged into AC power. In fact, some gaming laptops draw more power while gaming than the AC adapter can provide, and will slowly drain your battery when gaming even though it's plugged into AC.