Adding a new column to the custom database table in WordPress

add_new_column_to_wp_db.php

<?php
function add_new_columns_to_easyexam_students_exams () {
  global $wpdb;
  $table_name = $wpdb->prefix . 'table_name';
  // Check if column exists
  $column_exist = $wpdb->query("SHOW COLUMNS FROM $table_name LIKE 'column_name'");
  if ($column_exist == false) {
    // alter the table with the new column name
    $wpdb->query("ALTER TABLE $table ADD column_name VARCHAR(255) NOT NULL AFTER some_other_column_name");
  }
}

// Hook on plugin's activation and execute the above function
register_activation_hook( __FILE__, 'plugin_prefix_database_function' );
function plugin_prefix_database_function () {
  add_new_columns_to_easyexam_students_exams ();
  // and here you can add some more function that should be executed only once 
}