You would want either a fully custom "Python function" kind of API endpoint, or if your system remains close in spirit to a regular classifier, a "Custom Python prediction" enpdoint.
Both kinds of endpoints can access the data of a managed folder. You should put your CSV files into that managed folder. When you create the API Service package, the contents of the managed folder is taken with it, and your API endpoint code can reference it.
For more details, please see: