xbox turn off when playing a game

I am seeing this on the Xbox app when my console is turned off. When I turn my Xbox on it still says I'm playing the game. When I check my recent activity it is the last game I played before turning off my Xbox

for now when i want to play those games ill leave the xbox on, the problem appears when i quit the game or when the xbox is turned off.

however if i just turn off the console but not quit the game first then im able to continue, but in this case when playing the splinter cell conviction after a few days of playing it and turn off the xbox without quiting the game first the game forced me to start over anyway.

UPDATE

I finally tried my friend's XBOX One Power Supply Unit with my console and it works just fine.. No more shut downs, so the issue was with my power supply unit.

Now comes the most irritating part.

I called the XBOX One India Support and explained to them the whole issue..after few irritating minutes of useless troubleshooting which the agent was doing..he accepted that the problem is with the Power Supply and puts me on hold..then gets back to me
and tells me that the Power Supply Unit is out of stock and they cannot send a replacement unit..

Im now trying to find a vendor who can sell me the power supply unit as I do not believe that Microsoft will have it available anytime soon and I do not want to use my XBOX One as a Paper weight till then..

Seriously Microsoft don't you guys know that Power Supply Units, Controllers and other such common accessories are mostly the ones that need replacement shouldn't you have these over stocked in a country where the XBOX One Sales are so high???

According to one news channel it said that on the day one there were 200 units were delivered by Amazon.in to MUMBAI Alone..let aside the other big cities in India.

Hey there HefinTheGreat!

I'm sorry to see the power issue! You did a great job of explaining the issue, thanks! Since you mentioned you will try your friends power supply, that is a great next step. If you try that and it doesn't work, I will sadly have to recommend setting up a
console repair, you can do this by visiting our Online Service center to register and set up a console repair. If the power supply does work, then it's safe to say you just need to replace your power
adapter through the same sit I linked.

hi. I have a problem close to yours. I could do everything up till the games. I have a Xbox one S. I go on a game play for a couple mins. It turns off randomly and when I turn it back on it it shows the ventelation warning. So the more I try to play after
turning it on and playing, the quicker it shuts off.