Problem happened to me about 6 months ago. I took the phone into Verizon. They sent a new phone but for some reason the battery was not covered under warranty. Popped the battery into new phone... same bootleg issue. So then I bought a new battery (OEM off amazon) and the issue was gone. I tested it on both devices as I had not returned the 'broken' one yet. It is a battery issue.
I would not suggest buying the OEM battery off amazon. It looks like I got a refurbished one or possibly a counterfeit one even though I bought it from samsung on amazon. The battery was more snug than it should have been and it only charged to 80%. I would recommend spending your money on an Anker battery. https://www.amazon.com/Capable-Anker-T-Mobile-18-Month-Warranty/dp/B00PTVUWRQ/ref=sr_1_3?ie=UTF8&qid=1477493967&sr=8-3&keywords=anker+note+4