fix recording errors

I am recording classical baroque instrumental music.
I am not native English speaker, so I am missing some technical terms. I will try to explain in other words: when during a recording there is a mistake, if I want to play again only that beat and replace it in the original recording, how do I do that without let the hearer notice it?
I could not find any tutorial or thread about it, because I do not know the keywords to search for. In my language we call it “cut and saw”.
Thanks for your help.

In the land of tape that was crash recording. Play the tape forward until the mistake and then press record and start playing, covering up the mistake and everything after it.

We can’t do that.

What you can do is set a label at the place of the mistake with Control-M (I think). Then go back a beat and start playing again. Leave the recorder running. In post production, you can then locate the label and cut out the pieces not needed – including the mistake.

That’s very simple version of a complicated process, but that does work. You can do that in speaking, too:

“So, today I want to talk about the barbage…oops. [control-m] …I want to talk about the garage and the space-saving…”

In editing later, you would go back and find the label and then cut out everything between the first “I” and the second “I.”