IPhone 6s vibration/charging problem?

When my iPhone 6s is plugged in and charging it seems to vibrate when I rub the back with my hand. The battery also charges, and loses power very quickly despite the fact is it fairly new. Any ideas what is wrong with my phone, or how I can fix it?

Sounds like you need to get a newer longer lasting batty. They put the el cheapo ones in them when their new, just hoping they can sell you a new one later down the road.