The question is too general, but let me answer the question as it stands now.
Can the owner of the repo see when someone clones it?
No, they cannot. If I go to one of your repositories and clone it to my local hard drive, the owner will not be able to view that activity. And why would you want to? Likely there are many clones of your repository.
Know that clones can live on other systems than GitHub.
Now, will the owner know that someone forked their repository on GitHub itself?
Yes, they will, assuming they pay attention.
I did the following:
Logged in as my main account
Created a repository
Set up a new dummy-account on an alternate email address
Forked the repository I created earlier
Logged back into my main account
This is what I see on my first page after logging in:
If I do the following:
Click on my repository
Click on the small 1 to the right of the "Fork" button:
Click on the "Members" tab:
Then I see this:
Conclusion:
Yes, the owner of a repository will see when someone makes a fork on GitHub, but no, they will not see it when someone makes a clone somewhere else.
Open Github, find your repo, click on it. Then click on Insights and finally click on Traffic. Github shows a graph Traffic including git clones. Salutes!
As far what I found you CAN'T know when someone clones it (if you mean exact time) nor who cloned it.
But you can know how many clones were made on which date and the number of unique cloners from ths url.
However one thing I find fishy is unique cloners is more than unique visitors, how can someone decide to clone even without visiting the repo. I guess it may be bots in such cases.
As for now we can obtain this information with Rest API /audit-log,
but it is available only for Enterprise users with org:read permission.
We can see the actual users that have preformed fetch, clone and many more actions.