Can you be more precise about what exactly you want to achieve please? The API is the chess.com API - we don't 'create an API' as users of that.
Help with the API chess

You would need to know what technology your current website is in. If it's in the technologies you listed, you would want to make http calls using PHP to then display the data on your website. You could possibly make https calls and put the data in your own database as well.
Is the data for your leagues on Chess.com?

Hello,
I manage the only two leagues in the American continent. The PanAm daily chess league and the LCPAL live chess league. Only Chess.com.
Currently in the LCPAL league, I enter the data in a form and it is displayed on the website, for example see the Bala tournament:
https://livechessleagues.com/s3-bullet/
Something similar I need for the daily PanAM league.
My Hosting system is based on Linux, with CPanel.

The chess.com API is a REST type as I understand it, which means data can only be read from the site. At this time it's not possible to upload data to the site.

Ok,
So, ¿Is it not possible to store the data obtained from the Rest API in mysqli?
How does the world league page work?
I have knowledge of PHP, Mysqli, ajax, but I have not created an API. I need to update the data of my leagues on the website we have. Can anyone help us?