how to solve Invalid usage of the option NEXT in the FETCH statement
Upgrading to SQL Server 2012 will help but you'll still get the same error. From the documentation:

Limitations in Using OFFSET-FETCH:

ORDER BY is mandatory to use OFFSET and FETCH clause.
OFFSET clause is mandatory with FETCH. You can never use, ORDER BY … FETCH.


To return a non-deterministic 10 rows from your table you could do this in SQL Server 2012:
SELECT * 
FROM AM_API
ORDER BY (SELECT NULL) OFFSET 0 ROWS FETCH NEXT 10 ROWS ONLY;

If you cannot upgrade you have a few additional options. SET ROWCOUNT is not deprecated for SELECT statements so the following should work on SQL Server 2008:
SET ROWCOUNT 10;

SELECT * 
FROM AM_API;

SET ROWCOUNT 0;

You could also use a TOP expression:
SELECT TOP 10 * 
FROM AM_API;