API/SDK for sending email verification link after user registration from custom sign up page

I am having a custom sign up page which takes in user email and password. I want to send an activation link to user upon sign up. The user should get activated once the he clicks on the link and then get redirected to my application.

This is possible if we use okta sign up widget by enabling self service registration. But i want to have a custom sign up page.

Is there any api/sdk for this?
The activation link should not ask the user to reset his password. And i don’t want to create a user without password and then let user set his password upon clicking activation link.

Appreciate if any one can help.