Best resources for string searching or pattern matching exercises
Are you already familiar with the main algorithms in the area? Are you familiar with this site a huge and well-maintained list of references in pattern matching?

I don't see how one could come up with a list of exercised for string matching, except "implement all main approaches and test them on a lot of data". And data is really easy to come by: you can grab any text file and it will do (you can create a positive example by seeking to a random location in the text file and getting n characters, and for a negative example any random string will do).

I'd read up on KMP, Boyer-Moore, automata methods, and the naive algorithm and implement them, and then think about the problem trying to make your algorithms faster.

There is a huge literature in the area, of course, and the first link I posted can steer you in that direction.