How to get sub-genres for a particular podcast genre using podcast api?

Use GET /genres. You can cache the entire response data from this endpoint on the client side. Use the "parent_id" in the response to identify the hierarchical relationship among genres.

If you only need to get top-level genres, then pass the "top_level_only=1" parameter.

If you haven't used Listen Notes Podcast API yet, get API keys here - Get API keys