I created this forms and modal but the form don't work correctly. Can I send my program to anyone who can help me to solve this problem?

Your question is not clear, do you meet any error? Please explain more detail about your question and share the related code.

To open the modal, you can use Bootstrap 5 Modal, and you can create a partial view to create a new supplier and display the partial view in the popup modal, after clicking the create/save button, you can use JQuery Ajax to submit the form data to the action method and insert the new item into database.

Here are some resources, you can check them:

CRUD Operation on a Single Page in ASP.NET Core MVC

add record using partial view and bootstrap modal, But validation not work in asp.net core

AJAX In .NET Core

use jQuery AJAX method to call an Action method in ASP.NET Core