The client on the server is stupid

Help solve the problem, I can’t solve it for a week.
I make a platformer game for two players.
When I run the game for two players I have a server and a client (without a dedicated server).
Everything works fine on the client, but on the server the character that the client controls is twitching. For the experiment, I launched three players, everything is fine on all clients and on the server.
Question: why when I launch the game for two players on the client everything is fine and on the server the client’s character twitches.