You can use lftp for that, utilizing its mirror command. Here's a snip from the manpage:
mirror [OPTS] [source [target]]
Mirror specified source directory to local target directory. If target
directory ends with a slash, the source base name is appended to
target directory name. Source and/or target can be URLs pointing to
directories.
[cut...]
-N, --newer-than=SPEC download only files newer than specified time
--on-change=CMD execute the command if anything has been changed
--older-than=SPEC download only files older than specified time
[...]
Definitely have a look at the manual, as there are really many useful options to mirror - like --allow-chown, --allow-suid or --parallel[=N] for example. Lftp also works with other access protocols, like sftp, fish or http(s).