Steps to reproduce the issue

If a website with Joomla is hosted in Russia, then Joomla shows information about available updates, but can't update. Error appears: error:140770FC:SSL routines:SSL23_GET_SERVER_HELLO:unknown protocol

System information (as much as possible)

Standard shared Linux hosting with PHP 7.0.x, Apache 2.4.x, and Joomla 3.7.x

Additional comments

The problem happens, because the Amazon servers are blocked by Roscomnadzor (Роскомнадзор, http://eng.rkn.gov.ru/) - official organization that has the right to block any website for Russian Internet users. As a result, the Joomla can't reach the Amazon servers, and therefore, can't download the archive with updates.

Using wget via SSH leads to the same error:

 wget https://downloads.joomla.org/cms/joomla3/3-8-0/Joomla_3.8.0-Stable-Update_Package.zip
--2017-10-21 14:24:25--  https://downloads.joomla.org/cms/joomla3/3-8-0/Joomla_3.8.0-Stable-Update_Package.zip
Resolving downloads.joomla.org (downloads.joomla.org)... 72.29.124.146
Connecting to downloads.joomla.org (downloads.joomla.org)|72.29.124.146|:443... connected.
HTTP request sent, awaiting response... 303 See Other
Location: https://s3-us-west-2.amazonaws.com/joomla-official-downloads/joomladownloads/joomla3/Joomla_3.8.0-Stable-Update_Package.zip?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAIZ6S3Q3YQHG57ZRA%2F20171021%2Fus-west-2%2Fs3%2Faws4_request&X-Amz-Date=20171021T112458Z&X-Amz-Expires=60&X-Amz-SignedHeaders=host&X-Amz-Signature=180a0abc6390e1cc0634b25b2523dd7b4f70d845de21cc6b15d34f1af7e25b6d [following]
--2017-10-21 14:24:26--  https://s3-us-west-2.amazonaws.com/joomla-official-downloads/joomladownloads/joomla3/Joomla_3.8.0-Stable-Update_Package.zip?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAIZ6S3Q3YQHG57ZRA%2F20171021%2Fus-west-2%2Fs3%2Faws4_request&X-Amz-Date=20171021T112458Z&X-Amz-Expires=60&X-Amz-SignedHeaders=host&X-Amz-Signature=180a0abc6390e1cc0634b25b2523dd7b4f70d845de21cc6b15d34f1af7e25b6d
Resolving s3-us-west-2.amazonaws.com (s3-us-west-2.amazonaws.com)... 52.218.128.164
Connecting to s3-us-west-2.amazonaws.com (s3-us-west-2.amazonaws.com)|52.218.128.164|:443... connected.
OpenSSL: error:140770FC:SSL routines:SSL23_GET_SERVER_HELLO:unknown protocol
Unable to establish SSL connection.

The hosting providers confirm this problem, and can't help in this case. The only solution is to download/upload the updates manually via FTP. However, still in this case a problem of downloading the official update archive still exist. Technically, it's possible to use VPN to avoid the blocking rule, however, such approach is illegal and the government will punish for breaking the law and using the VPN.