I want to use PsqlConnection to connect to Pervasive database.

For example:
public PsqlConnection myConnection;
myConnection = new PsqlConnection("Server=myHost;ServerDSN=DEMODATA") ;
myConnection.Open();

I want to access a Pervasive database from an ASP.NET application. The asp.net application and the database are not within same box (i.m. the web application and Pervasive SQL database are on different computers across the Internet.

How do I create “ServerDSN” from the webbserver or is there any other way to connect to the database?

The ServerDSN is the Pervasive Engine ODBC DSN on the machine where the Pervasive engine is running.
You won't create the "ServerDSN" on the webserver but you would create it on the Database server.