If you're just thinking "a shop that develops APIs", that is the same as "a shop that writes code". You are not offering the client anything tangible they can identify. Unless you restrict your clients to software houses without the time or expertise to write their own APIs, the larger non-developer world of clients has no idea what you are offering.

I write APIs. I specialize in them, but for a specific purpose. I develop 3d animation technologies and then expose them via an API. I then license use of that API to 3rd parties, hosting the servers in both cloud and colocation. That is something tangible they can grasp. This is after spinning my wheels for a while trying to do what you seem to be thinking.