I have a battery with less than 2.1A can I use that?

Yes, you can but the lower power input, the shorter the continuous power supply such as video recording time. For 5V 2A, we are confident that it is enough to power to continuously video recording with no stops. If you’re using a 5V 1A or 5V 500mA external battery you may have to break a moment if the Case Relay battery is empty.