The effect of the electroweak sphaleron transition in balance between baryon excess and and the excess of stable quarks of $4^{th}$ generation is studied in this paper. Considering the non-violation of $SU(2)$ symmetry and the conservation of electroweak and new charges and quantum numbers of the new family, it makes possible sphaleron transitions between baryons, leptons and 4th family of leptons and quarks. In this paper we have tried to established a possible definite relationship between the value and sign of the $4^{th}$ family excess relative to baryon asymmetry. If $U$-type quarks are the lightest quarks of the $4^{th}$ family and sphaleron transitions provide excessive $\bar U$ antiquarks,
asymmetric dark matter in the form of dark atom bound state of ($\bar U \bar U \bar U$) with primordial He nuclei is balanced with baryon asymmetry.

The main scope of our current activity is to deduce the relationship between baryon excess and excess of stable fermions of $4^{th}$ family. We can take for definiteness that $4^{th}$ neutrino and U-quark of $4^{th}$ family are stable and establish the relationship between their excess and excess of baryons and leptons by sphaleron transitions. The aim is to find conditions at which observed baryon excess corresponds to such an excess of $\bar{U}$ that explains observed dark matter by $(\bar{U} \bar{U} \bar{U})He$ atoms.