Kindly suggest an inverter regulator which can give -1V from 5V battery with least supply current.
You can start with LT8330: low IQ part with 1A switch. There are several inverting regulators in my search in link below.
Please confirm part LT8330 will support -1V output. What is the output voltage range LT8330 will support .
-1V should be ok. Please refer to Inverting Converter page 15 of the datasheet. The output voltage will be limited to the MIN off time of 65ns in page 3 of datasheet. At 5VIN 2MHz operation, output voltage may go around -25V (considering margin).