Rule out planets first, otherwise it depends on which constellation Venus, Mars or Mercury are in.
The closest extrasolar object to the Earth is the South Gate Eelsen, but it belongs to Centauri, not the zodiac.
The next nearest star is Barnard, located in Ophiuchus, belonging to the zodiac constellation mentioned by the subject, 5.96 light years away from the earth.
Fortunately, I only counted to the second star and solved the problem. If you are interested, you can check the list of 10 and 50 stars nearest to the earth.