Pilot reported the APU was possibly sending smoke into the aircraft while at the gate.

Narrative

At approximately XA:00 local time I felt the air conditioning seemed to stop putting out as much air as it had been and started to notice a slight burning smell. As I was noticing the smell the captain said do you guys smell something burning? The Flight Attendant and I both affirmed the smell and we immediately shut down the air conditioning packs and APU and closed the APU bleed. Their was some smoke that came into the cabin and the flight attendant got the people who had just started to board the plane back off. On the flight deck we went through the Cabin or Flight Deck Fire/Smoke/Fumes; Air Conditioning Smoke; and Smoke Removal checklists. The Captain then proceeded to call ops to ask for CFR (Crash Fire Rescue) and then called Maintenance. I went outside to see if I could see anything that caused the issue. One ramper told me he saw smoke coming from the APU exhaust and another told me he heard a grinding noise from the area of the APU. I could see a small amount of smoke coming from the APU exhaust. I reported back to the captain with that information and we gave that information to maintenance. We never got any fire indications on the EICAS (Engine Indicating and Crew Alerting System) or overhead panel.