If in 24 hours durations the sun appears only at a short moment which means the rest moment is dark, for RET, aren't most zodiac constellations supposed to be visible? Because our sight (mostly) ain't be blocked by the sun's ray.
When the sun is up for only a short while, the constellations the sun is in, or near, are also up for only a short while. Since the sun is close to them, it's either day or twilight while they're up, so the sky is too bright to see them.
Or are some zodiac constellations visibility affected by their distance?
Whether or not some constellation is ever above the horizon at any time of day or night depends on its declination and your latitude, not distances. From places north of the Arctic Circle some of the southern zodiacal constellations are never above the horizon, so even if it's dark for 24 hours you still can't see them. Similar for south of the Antarctic Circle and the more northerly constellations of the zodiac.