My battery and charger guide for the Sony a7III covers all you need to know about which batteries and chargers are supported, both original and third party.
Sony a7III Battery and Charging Advice From a Pro
Created specifically to support working professionals in the fields of sports photography and photojournalism - the Alpha 9 II delivers unmatched performance including blackout-free continuous shooting at up to 20 frames per second with Auto Focus and Auto Exposure tracking at 60 calculations per second - plus continuous shooting at up to 10 fps with mechanical shutter.
Sony A9 II Digital Camera Body
Sony Battery NP-FZ100 Charger BC-QZ1 for Sony Alpha A7 IV ILCE-7M4K/7M4 & A7 III
Recommended Third-Party NP-FZ100 Batteries & Chargers for Sony
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Sony A7 III Battery and Charger Guide
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Sony NPFZ100 Z-series Rechargeable Battery Pack for Alpha A7 III, A7R III, A9 Digital Cameras black : Electronics
Powering Options for the Sony A7S III/ A7 IV
Help Guide Charging the battery pack while it is inserted in the camera
NEEWER NP-FZ100 Sony Replacement Battery Charger Set - NEEWER
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Battery and charger options for the charger-less Sony a7 III - Newsshooter