You can set a custom price for your customers now, to do so you need to create a service with a defined price which will be for all the customers.
Read this article to know about how to create services.
After service is created, go to the customer profile for whom you want to set custom price, navigate to Custom Price tab and click on 'Add Custom Price'.
Navigate: Customer > Edit > Custom Price > Add Custom Price
Select the service for which you want to set a custom price and add the custom price. Click on save once done.
Once this is done, you can go ahead and create appointments and you can see the custom price applicable to the customer and for others, it's still the standard price you defined in services.
Note: The changes will be applied for the appointments created after the custom price is set, appointments created before will be left unchanged.