403 error while creating the repository on GitHub

Could anybody help me, please?

What version are you on? GitHub has changed its security algorithms support, so we re-issued all recent releases to include this fix.
https://blog.jetbrains.com/blog/2018/02/26/update-on-ssh-access-to-github-in-intellij-based-ides/
Also, does pulling work?
And it would be nice to look at the log after a push attempt.

Thank you, Eugene. My version is 2018.1. Pulling works fine.

It's not the case then. Could you please share the IDE log after a project creation attempt? (It'd be better if you upload it somewhere)

How can I get the log?

Sorry, should have posted the link.
https://intellij-support.jetbrains.com/hc/en-us/articles/207241085-Locating-IDE-log-files

2018-04-29 08:38:40,595 [38786234] INFO - #git4idea.commands.GitHandler - [gllacy] git -c core.quotepath=false -c log.showSignature=false push --progress --porcelain origin refs/heads/master:master --set-upstream

2018-04-29 08:38:41,569 [38787208] INFO - #git4idea.commands.GitHandler - remote: Permission to mikhin/gllacy-html.git denied to undgrnd.

2018-04-29 08:38:41,569 [38787208] INFO - #git4idea.commands.GitHandler - fatal: unable to access 'https://github.com/mikhin/gllacy-html.git/': The requested URL returned error: 403

In the second line I see "denied to undgrnd.", but I have another user in PHPStorm GitHub settings (exactly "mikhin").

Could you help me, please?

Hi,

Does Test button in Settings | Version Control | GitHub work fine?

Yes, it does.

Is there a dependency from git settings out of PHPStorm?

Yuri, as it already takes more time that it should, and it's definitely a shame for us, could you please re-submit this issue as a support ticket?
Please reproduce the issue and attach the full IDE log there, not just a snippet - you'll get much more timely updates this way.

https://intellij-support.jetbrains.com/hc/en-us