Prestashop on Apache + Nginx as proxy + Fast-CGI - Web Services API error 401

[adi5497]

I'm trying to config a PrestaShop on VPS. Everything is working, despite one, web services API. When I'm trying to go https://example.com/api, web services ask me about auth key. After entering it into username field and leaving password blank, it works. But while I'm trying access to API via remote app I'm getting error 401 unauthorized. I know that it's server fault becaus on previous host everything worked fine. I'm useing Debian 9 and Apache 2+Nginx as proxy+PHP 7.0 with FastCGI. Where could be a problem?