Welcome to the forums,
(Moved from ZD section.)
POP?
In 5.0.6+ you can set this via CLI/SOAP/JAVA:
Quote:
su - zimbra
zmprov ma user@domain.com zimbraPrefPop3DownloadSince 200812151000000Z
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In 5.0.7+ ZWC > Preferences > Mail > Allow only mail from now to be downloaded:

(The web-client setting doesn't yet allow custom time like you can with the CLI.)