Hi Jenilyn,
You can use the external API in custom web part like we do in any other asp.net user control. Just create a new web part using this link and register your new user control inside Kentico. You can call external API on web part page load or any other button event based on your requirement.
To display data in page you can bind the response from external API to repeater or any other control according to your layout design, see this link for repeater reference.