If you are using zsh you can enclose in parenthesis () a list of so called glob qualifiers which select desired files. In your case, that would be
cp *(On[1,4]) ~/
Here On sorts file names alphabetically in reverse order and [1,4] takes only first 4 of them.
You can make this more robust by selecting only plain files (excluding directories, pipes etc.) with ., and also by appending -- to cp command in order to treat files which names begin with - properly, so:
cp -- *(.On[1,4]) ~
Add the D qualifier if you also want to consider hidden files (dot-files):
cp -- *(D.On[1,4]}) ~