The equivalent is debsig-verify, which verifies embedded signatures in .deb packages using locally-stored keys and policies.
Unfortunately this isn’t useful in general because Debian packages are usually not signed individually; in fact, as far as I’m aware, the Debian archives reject individually signed uploads. Debian signs repositories as a whole, rather than individual packages, which means that packages can be verified as they’re downloaded, but not necessarily afterwards. (See How is the authenticity of Debian packages guaranteed? for details of repository authentication.) apt will verify packages before installing them, using its locally-cached information and locally-stored keys, but I don’t think there’s a way to ask it to verify a package as a separate task.