In the context of the rapid development of new medical technologies, the problem of protecting the rights of citizens and ensuring respect for human dignity is becoming increasingly urgent. The authors come to the conclusion that the protection of the patient’s rights when using genomic technologies can be carried out in the order of claim proceedings. Typical methods of protection are recovery of damages in the event of injury to health, compensation for moral damage in connection with the violation of such non-material benefits as life, health, physical integrity, privacy. Particular attention is given to the problem of children’s rights protection when using genomic technologies, including the right to natural biological origin, the right to know their biological parents and family (genetic) history, since the use of advances in genetics and biomedicine by one generation of people can be a serious challenge to the existence of fundamental freedoms and equality of future generations.At the moment, states should define the limits of possible intervention in the sphere of private (parental) arbitrariness in order to prevent future harm to children born with the help of modern technologies. Consideration of individual problems of the rights of citizens protection when using genomic technologies indicates objective difficulties in finding solutions due to bioethical principles, the need to ensure a fair balance between the interests of the parties to the relevant relationship and third parties, and the need to minimize potential risks. The breakthrough achievements of medical and biological science pose an important task for the state to develop an effective system of legal guarantees aimed at ensuring respect for human dignity, protecting the rights and interests of an individual, preventing the biotechnological construction of a person for the purposes of eugenic practice, etc.