Terminals and terminal emulators do not pass keystrokes that ultimately get to programs (e.g. to a
tmux client), they pass a stream of bytes. Some keys (or combinations) generate single bytes, some keys (combinations) generate (more or less standard) sequences of bytes. AFAIK there is no standard byte or sequence uniquely assigned to Ctrl+3. Upon Ctrl+3 a virtual terminal (e.g. tty4) prints just 3 for me. konsole generates the escape character. What does your terminal (terminal emulator) generate? Run e.g. xxd, then Ctrl+3, Ctrl+d, Ctrl+d. What is the output?