cleaning my fossil leather purse

Actually you are in a wrong place - this is where we fix watch and clock related problems.
But there is one advise I can give you:
All good/respectable shoe shops sell special cleaning fluids for many different types of leather. Do not mind these are shoe shops, as shoes, bags, purses, belts and so on are made of same source- leather.
So, take your purse with you and visit one of these shops. They will give you advice what's best for your particular purse. You can buy special spray as well - it will help to keep all dirt and grime at bay in future.

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