C#
The #1 place to put your effort is advanced C#. The more you know about C#, the easier it will be to create world-class APIs. Pay particular attention to Linq as much of your retrieval code will make extensive use of it. Even if you don’t write in Linq, other API creators will, and you’ll need a solid working knowledge of Linq to understand their work.
SQL
The next most important place to put your effort is expanding your SQL skills. The API programmer is, very often, called upon to retrieve the requested data from a database, and in most cases, that will require a working knowledge of SQL.
Note that there are different flavors of SQL depending on what database you are using; however, the core of SQL is the same across platforms.
Database
In addition to expanding your SQL skills, you will want to become as proficient as you can in the database platform you’re working with (e.g., Entity Framework). As noted previously, the SQL you’ll use...