Golly by gosh! While I'd really like to try to answer your question, there's really not enough information here and it's rather difficult to follow.

What's the refrigerator have to do with with this, unless you are trying to power it off a 12 volt battery with and inverter.

BTW, the refrigerator may consume only 331 watts while running but may require up to 20 amps to start the compressor. But then, what size refrigerator are we talking about?

As far as recharging a 12 volt battery:

What is the voltage output and current output of the generator? What is the amp-hour rating of the battery? How far has the battery been discharged?

The inverter would be used to convert the 12VDC to 120VAC and usually has an overhead of at least 10-15% in excess of the load.

A little more information is needed here, but running a fridge off an inverter from a 12 volt battery, being charged by a 60 watt generator is just not going to happen.