When i plug my note 9 on charging with genuine samsung adapt fast chager and genuine samsung cable. Sometimes it shows "check charger connection" and fast charger gets disabled and cable charging gets activated.
With your quotes, I think it is due to irrelevant back cases... Try removing the back case and charge your phone and it may charge properly with fast charging...
And a common advice for charging is keep your phone idle for at least 10 minutes before and after charging and the phone temperature less than 30'C. If possible try charging your phone in cool environment...
Please perform the below mentioned steps to resolve the issue:
1. Check your charging cable (USB cable) for physical damage such as wear and tear, bent prongs etc. If it is damaged then kindly visit your nearest service center to get it replaced.
2. Check charger functionality, try to charge your device with some other charger or use your charger to charge some other device.
3. Check charging, if rating is 15W or above. Kindly try to charge the device in a non-inverter socket.
Note: Kindly open Device care from Settings > Battery > Please tap on 3 dots(more option) at the top right hand side > please select settings > enable fast cable charging.
For further assistance, register your concern in Samsung Members Application (Open Samsung Members Application > Get help > Send Feedback > Error report/Ask questions).
