If high nybble of each byte is always exactly zero, then obviously you can't lose entropy by discarding it: the random output of any one-to-one (deterministic) function of a random input has exactly the same entropy as the input. But the story doesn't stop there.
First, you should have a probabilistic model of the entropy source, and a collection of probabilistic models of ways it could fail, informed by physics and engineering. Part of your model might include that the high nybble of each output byte is zero: if that changes, could that be evidence of a failure mode in your understanding of the physical device?
You should devise a test to distinguish the null hypothesis that your device is working from the collection of alternative hypotheses that your device has failed, with high true positive rate or statistical power to report failure, and with whatever false positive rate—often confusingly called ‘statistical significance level’—you are willing to tolerate. This lets you raise an alarm when the device has broken.
This test should be informed by the specific details of your device. Generic tests like dieharder or the NIST entropy suite or what have you are designed in ignorance of your device. They can detect some particular deviations from uniform, like if the ratio of zero bits to one bits is excessively far from 1/2, but they're very limited because the designers had no idea about the particular device you have in your hands. (More details on what generic ‘entropy tests’ can do.)
But don't worry about using the bits from the entropy source directly, or about whatever your favorite measure of nonuniformity is, as long as the probabilistic model for the device can generate samples with at least ${\geq}256$ bits min-entropy—if you have to read a kilobyte out of the device to get that, so be it.
Next, you should feed the output through a standard preimage-resistant hash function like SHA3-256 (‘conditioning’).* You can lop off the high-order zero bits first if you want, or not: it doesn't matter, if you're 100% sure in advance that they will be zero. As long as the input has ${\geq}256$ bits of min-entropy, the output can essentially be treated as if it has 256 bits of min-entropy, or as if it were a uniform random string.
My idea is simple - throw out each higher byte from each sample (the one which is mostly zero) and leave just the lover one. The question is, is this OK? Can i still treat such stream as unconditioned?
If you are 100% sure that they will always—in functioning and broken devices—be zero, then yes. The point of the unconditioned rule is that after conditioning like SHA3-256, statistical tests are essentially useless. You can test guesses about exactly what string of bits the device produced, but that's all. In contrast, if you're simply discarding bits of output that you can predict in advance will be zero, then that can't hurt your ability to distinguish a working device from a failed device based on the physics.
Unless, of course, one of the failure modes causes the bits have become one when they should have been zero, in which case, well, don't discard them—test them!
* There is literature on a subject called ‘randomness extractors’, typically constructed out of universal hash families like multiplication by a uniform random matrix. These are theoretically kind of interesting objects that aim to illuminate how much min-entropy you need in a nonuniform distribution to get within a certain total variation distance of a uniform distribution. But in practice, randomness extractors per se are essentially useless, because in order to use a randomness extractor to massage a nonuniform distribution into more-uniform, you need to also already have a uniform distribution on the extractor seed. With that uniform random seed you could have just done normal cryptography. (More details on randomness extractors and practical cryptography.)
