My problem is I want to create a field of type "File" in a custom list. But my lists content type is "Item" which doesn't support such type of fields. The point of this manipulation is to update a field in my custom list from a field of type "File" in a document library using SharePoint Designer
There is no "File" Content Type. You can watch the available Content Types under Site Settings -> Site Content Types. If you want something different you have to create your own Content Type.