It sounds like you installed the ODBC driver, did you point it at your ODBC enabled FM Server? I'm not sure how you want to use it in conjuction with MySQL, but most deployments I've worked with typically connect the pieces at the application level. I guess it depends on the problem you are trying to solve.
I use FileMaker as a JDBC Datasource. That might be easier
> I wan to use Filemaker database via ODBC Connection
When you created the DSN, did you test the connection? Did it succeed? If so then the DSN is ready to go.
How you use it in your other environment depends on how you can consume a DSN or DSN-less ODBC connection. What scripting or coding environment do you use?