Setting up SMTP mail distribution?

Question

Email

Hello!
I have a forum on phpBB 3.0.12.
When setting up mail in the admin panel, I specify the mailbox data from the hosting account (the mailbox is needed to send notifications). After entering the information, I save and make it so that he should send a notification to my mailbox, but it does not come. In the logs, it indicates that the hosting server refused to send.
Tell me, please, how can I send mail not through a hoster? Are there any smtp or services where I can attach my domain and send emails through it?
phpmail function also does not work for some reason, but there are no errors in the logs.

Answer 1

pdd.yandex.ru - attach domain mail (domain DNS is also possible), create a mailbox, send letters with authorization through it.

Answer 2

Are there any smtp or services where I can attach my domain and send emails through it?

It is not necessary to attach a domain (unless, of course, you need to send emails from your own domain). The main thing is that the service would provide SMTP access (as far as I remember that Google and Yandex allow this). Authorized - send.