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Studies of low-mass dwarfs in voids are substantially under-represented. Recently published sample of 1350 galaxies residing in nearby voids (R < 25 Mpc, Pustilnik et al. 2019) allows one to advance in study of their properties. We present a progress report on the ongoing project of the systematical search for and studying rare unusual void dwarfs. They combine the extremely low gas metallicity (XMP, Z~Zo/50-Zo/30), very low mass-fraction of stars (M*/Mbary~ 0.01-0.03) and non-cosmological ages of the main stellar population (typically, T~1-3 Gyr). These properties suggest the initial evolutionary state, and thus, their late formation and/or very low star formation rate. In course of this project we found eight new such objects. Their finding presents challenges for current state-of-art simulations in near-field cosmology. The non-cosmological ages of the main stellar population directly relate these kind of void dwarfs to the predicted in simulations Very Young Galaxies (VYGs, Tweed et al. 2018). Number fraction of VYGs is expected to strongly depend on cosmology with different types of DM. Therefore, statistics of such objects can help to constrain type of DM. Besides, finding of such unusual dwarfs in voids needs more detailed model predictions of void galaxy properties with baryon masses of 10-100 million Mo.