The only way someone can make a move in a game is if they have access to the account. If you think someone has your password, you should change it.
Also, just in case you may have accidentally moved the pieces yourself you should turn on move confirmation if you haven't already.
Thank you for your answer but I use facebook login to access chess.com and confirmation is of course turned on. That's why I'm so surpruised. I don't think i made the same mistake twice. I wonder if someone can check IP addresses, from where moves were made. I play this tournament from Georgian and Czech IPs.
I'm not sure that is tracked but you could open a ticket to see.
https://support.chess.com/customer/portal/emails/new
I play the 36th Chess.com Tournament (1801-2000). In on of the party, in which I played in black, someone moved my queen when my knight was attaked by pawn. At first, I thought it was my mistake and resigned, but then in another game, with the same player, where I played as white, again wrong move was made, my white bishop killed the pawn which was defended by knight and bishop. I think someone plays that wrong moves instead of me. Is there any protection against fraud?