Sorry, yesterday I wrote something weird. Lets start over.

I have 3 mailboxes set up in Kmail, everything works fine I can receive, send, filter my mail. Now I want to add fourth mailbox. I've entered my mailbox name, password, server for sending and receiving (SMTP and IMAP, with STARTTLS with corresponding ports, "Plaintext" for receiving and "Login" for sending).
Setup went well, the mailbox is indicated as online, but my inbox is empty. I see letters in "Sent" and "Trash" folders, I can even send letters, But Inbox is steel empty. Tried to change ports, change to SSL, Nothing helps. If I change authentication from "Plaintext" to "Login", then server rejects connection, and mailbox goes offline. What else to try?

Tried to setup this mailbox in Evolution and Thunderbird with the same settings, everything is working. I see my mail in Inbox,

I use Manjaro Linux (Akonadi and Kmail 16.12.3-1)

Hi!

I cannot really help you with kmail, but you may have a look at the serverside subscription and try to get the folders one by one. Right-click your new mail account -> serverside subscription -> enable it and select the single folders.

Perhaps it could help starting kmail from terminal to get some messages while fetching the new account.

Another approach would be to check akonadi messages.

Hm, I don't know what can I do with Akonadi itself, but I tried Kmail in Konsole. Here is the output when I sync INBOX and whole mailbox:
org.kde.akonadi.ETM: collection: "INBOX"
org.kde.akonadi.ETM: Fetch job took 82 msec
org.kde.akonadi.ETM: was item fetch job: items: 0
org.kde.akonadi.ETM: collection: "mymail@server.smthng"
org.kde.akonadi.ETM: Fetch job took 53 msec
org.kde.akonadi.ETM: was item fetch job: items: 0
There is no difference with other mailboxes, only time changes a litle bit.

If I sync whole Kmail i get
"Item query returned empty result set"
What does it mean?

Solved. Somehow Kmail rejected subscription for INBOX and some other folders. Whan I deed:

On INBOX folder RMB - "Serverside subscription" - checkbox on needed folders. (Thank you koffeinfriedhof for pointing me to that, I thought I already deed this before)

Why Kmail rejected subscription for main mail folder? I deleted and reset this mailbox several times, while experimenting, and every time Kmail just ignored INBOX? Weird.

Second problem. I use KDE in Russian. And in Russian translation options "Manage local subscriptions" and "Serverside subscriptions" translated unclearly and I thought that it is the same thing.

You may want to file a bug on bugs.kde.org if you feel the translation is unclear, so that translation teams can hopefully fix it.