To run a mini fridge from a battery, solar panels and an inverter you would you would need an inverter that can provide up to 800 starting watts and around 300 to 300 continuous watts to be safe.
Most mini fridges use between 100 to 150 watts of running power but you also have to factor in that you need at least 300 to 500 starting watts.
The mini fridge compressor needs extra wattage and amps to get started and then as it's running it uses less power.
The watts of a refrigerator depends on the size of the refrigerator.
For example a large household refrigerator will use 200 watts and some as low as 100 watts.
However it can take 400 to 800 watts to get the refrigerator compressor started so you need to factor in the starting watts and amps of the refrigerator as well.
The running watts of the large refrigerator are usually between 100 to 200 watts but some may use as much as 500 to 800 watts.
A mini fridge would use around 100 watts to 150 watts and may need 200 to 300 watts to get started.
If you're running a mini fridge off an inverter you would need an inverter that can provide up to 800 starting watts and around 300 to 300 continuous watts to be safe