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The rotation period of Venus is however about the same as its orbital period, inferring a tidal lock with the sun. Such a tidal lock may have likely inhibited core rotation as well. Then again Mercury has a weak field, and is in a similar tidal lock situation.

Let me check some info on the Jovian moons, as in small bodies in close proximity with the central object of the system.

Jovian moons:
As an example, Ganymede and Callisto, two of the large (Galilean) moons. Ganymede and Callisto are both in tidal lock with Jupiter, so their rotational periods are in sync with their orbital periods. Ganymede has an iron core and a probable subsurface ocean, and also has its own independent magnetic field. Ganymede is close enough for Jupiter to exert some tidal heating - keeping the core liquid?
Callisto, while in tidal lock, not so much to cause tidal heating. However Callisto is theorized to have a silicate core. Callisto may also have a subsuface ocean, enough so that it locally influences the magnetic lines of force from Jupiter’s field, since the water - with dissolved salts - being an excellent electrical conductor. But it does not have its own independent field - as found by various probe missions.
Europa is anothe moon that is also in tidal lock, has a subsurface ocean, and an iron core, likely solid. No independent magnetic field, just an induced field due to Jupiter’s field for the same reason as Callisto. Europa is the smallest of the Galilean moons, so perhaps its mass is not enough for tidal heating to keep the iron core in a liquid state.
Io is the closest of the Galilean moons, and is subject ot a lot of tidal heating - thus its volcanic activity and sulfur plums. Iron core, but no independent field (however the flux from Jupiter may be overwhelming any measurement of a field from Io, but for now the core of Io is suspected of being non-convecting, therefore solid (? )). Io is a strange beastie though.