It is quite hard to find clips using https://www.twitch.tv/manager/clips page to find clips and API does not offer nice solutions to make a 3rd party application to replace it.
Here are some examples of API request parameters and some of their possible uses.

curator_id:
- clip creator can find all their own clips
- broadcaster can find and delete all the clips from problematic viewer

vod_id:
- find clip compilation material for the stream

created_at:
- find clip compilation material for the date(and range)
- find throwback clips - "last year this time we did this"

broadcaster_id:
- in combination with others would make the API request more useful