How to test void method which returns single instance of a class?

I'm setting up new java project , i have a void method in database class which returns single instance of the object (singleton class). I want to test it using junit and mockito.

I have tried the fallowing testcase code using assertSame which return's the test fails.

public class DatabaseConnectionTestCase {

        DatabaseConnection connectoin;
        
        @Before
        public void setup()
        {
                connectoin = DatabaseConnection.getInstance();
        }
        @Test
        public void test() throws SQLException 
        {
                Assert.assertSame(connectoin.GetDBConnection(),connectoin.GetDBConnection());
                
        }

}

Database class which is used for testing

   public Connection con = null;
public static DatabaseConnection Database_single_instance = null;

// create single object for all the class
public static DatabaseConnection getInstance() 
   {
    if (Database_single_instance == null)
        Database_single_instance = new DatabaseConnection();

    return Database_single_instance;
}

private DatabaseConnection()
{

}
// establish a database connection used across the project
public Connection GetDBConnection() throws SQLException {

    String url = "jdbc:mysql://localhost:3306/iteration";
    String username = "root";
    String password = "";

    try {
        Class.forName("com.mysql.jdbc.Driver");
        con = DriverManager.getConnection(url, username, password);
    } catch (ClassNotFoundException e) {
        // TODO Auto-generated catch block
        e.printStackTrace();
    }

    return con;
}

// return connection as single instance
public Connection getConnection() {
    return con;
}