Filtering out, a list of games, based on their followers
f-strings
I recommend to use f-strings (Python version &gt;= 3.6) for string formatting. See this link for more details:
https://www.python.org/dev/peps/pep-0498/
When you use them you can replace
if month1 &lt; 10:
    month1 = &quot;0&quot; + str(month1)

with an expression like this:
month1 = f'{month1:02}'

This adds a leading zero if month1 only has one digit.
In addition, an expression like:
 Url = (
        &quot;https://api.rawg.io/api/games?dates=&quot;
        + str(year1)
        + &quot;-&quot;
        + str(month1)
        + &quot;-&quot;
        + str(day1)
        + &quot;,&quot;
        + str(year2)
        + &quot;-&quot;
        + str(month2)
        + &quot;-&quot;
        + str(day2)
        + &quot;&amp;page=&quot;
        + str(PageNumber)
        + &quot;&amp;platforms=4,187,1,18,186&amp;page_size=40&amp;ordering=released&quot;
    )


can be written as
url_part1 = &quot;https://api.rawg.io/api/games?dates=&quot;
url_part2 = &quot;&amp;platforms=4,187,1,18,186&amp;page_size=40&amp;ordering=released&quot;

 Url = f&quot;{url_part1}{year1}-{month1}-{day1},{year2}-{month2}-{day2}&amp;page={PageNumber}{url_part2}&quot;

using f-strings. This is shorter and less error prone (less quotes you can forget), opinions might vary regarding the readability, though. Type conversions (str(.)) are not needed anymore.
Avoid hardcoding
It is good that you added a comment to explain where the number 40 comes from:
AmountOfPages = AmountOfGames // 40 #1 page contains 40 so it does amount//40 to get pages

However, it would be even better if you assigned this number to a variable with a telling name. For example
games_per_page = 40 # Preferably, put this on the top of your script or in a config file
# [...]
AmountOfPages = AmountOfGames // games_per_page

This is more flexible. Imagine the number of games per page changes.
Leftover page: ceiling division
In this part you first do a floor division (//), then you add 1 for leftover pages
AmountOfPages = AmountOfGames // games_per_page#1 page contains 40 so it does amount//40 to get pages
if(AmountOfGames%games_per_page != 0):
    AmountOfPages = AmountOfPages + 1 #does +1 if there's a leftover page

This can be simplified with a ceiling division
import math

AmountOfPages = math.ceil(AmountOfGames / games_per_page)