I would start by holding all three physical buttons for a full 3 minutes (phone switched off) to fix battery logic problem. this resets the battery logic on some phones and how the battery talks to the software to let it know how much power it has based on the voltage. After that start the phone (may take some restarts ) and charge the phone
Next, eliminate Battery Problem by changing battery
A) Battery lived it's life. If the battery is removable, borrow a battery if possible and see the behaviour. Check if it is bulged. Easy way for this is to keep the battery on a flat surface and try to spin it. If it "spins", it is due to battery bulging and changing battery is indicated
B) Battery has a chip that provides phone health and condition to device. Based on this information, device takes actions such as stopping the charge, LED notifications to show battery charged etc. Changing battery will also rule out possibility of this chip having gone bad
Fix OS problem. Fuel Guage drivers ( part of software in your device) corrupted. To rule this out, i suggest back up your data and with your recovery wipe clean all Cache and system and flash stock ROM (requires root). If not rooted, try a factory reset (deletes data, so back up before this). Our else if Kies supports reflashing ROM, do that. If the problem continues, it is likely that it is not a driver corruption issue.
Fix Hardware problem of device Hardware of battery charging chip gone bad. Less probability and best handled by service center
Getting to the root of the problem takes time and I would proceed in the order suggested. All the best and do post the conclusion, it may help others having similar problem with your device make