There was no property management company and no property fee before. Is it legal for the new property company to charge the previous property fee?

That depends on whether the property company that asked you for the property fee has performed the property management related work for you. After verification, it is unreasonable to charge you property fees now if you don't have actual property services in your area. You can refuse.

Furthermore, if it is the house you rent now, it depends on the specific terms of the lease contract between you and the landlord. The responsibilities and rights of renting a house, your rights and obligations must be clear. Then we can know the specific operation method.