How can I send my device ctrl+c through serial port in C#?
Serial ports don't transmit keys. They transmit bytes, which are normally the ASCII representations of characters.
"Keys.ControlKey & Keys.C" has to do with sensing what is going on on a PC keyboard. But serial ports do not transmit the whole state of the keyboard. For instance, the F keys and the arrows are entirely outside the ASCII system.
An ASCII chart will tell you that, for instance, Ctrl-A is 1, Ctrl-B is 2, Ctrl-C is 3, 'A' is 65, and so on.