To change the log level for a custom API in an OSGi environment, the appropriate configuration to modify is the Apache Sling Logging Configuration. This configuration allows developers to adjust the log levels for specific packages or classes, providing the necessary control over logging output. The other options, such as Apache Sling Log Tracker Service, Apache Sling Logging Writer Configuration, and Adobe Granite Log Analysis Service, do not directly relate to setting log levels for a custom API.