How to raise locally, an existing site working through SSL?

Question

Digital certificates

Good afternoon, dear community of technical experts.
The question is the following, there is a site on the Internet, I was asked to correct it. It runs on begget using an SSL certificate. Previously, I did not have problems with certificates. Naturally, as a normal white person, I did not pick it in a combat state, but decided to clone it for myself and edit and test it on a local server before sending it to the Internet. I set up the server environment and even self-signed certificates, new projects that I create are displayed with a bang via https, the site cloned from the Internet is not in any, I've been fighting for the second day, tell me where to dig?