I have already written a script that opens Firefox with a URL, scrape data and close. The page belongs to a gaming site where page refresh contents via Ajax.
Now one way is to fetch those AJAX requests and get data or refresh page after certain period of time within open browser.
For the later case, how should I do? Should I call the method after certain time period or what?
You can implement so-called smart wait.

Indicate the most frequently updating and useful for you web element
at the page

Get data from it by using JavaScript since DOM model will not be updated without page refresh, eg:
driver.execute_script('document.getElementById("demo").innerHTML')

Wait for certain time, get it again and compare with previous result. If changed - refresh page, fetch data, etc.
Python Selenium: How to get fresh data from the page get refreshed periodically?