Background: Hemoglobin is a tetramer consisting of two α-chains and two β-chains of globin. Hereditary aberrations in the synthesis of one of the globin chains are at the root of thalassemia, one of the most prevalent monogenic diseases worldwide. In humans, in addition to α- and β-globins, embryonic zeta-globin and fetal γ-globin are expressed. Immediately after birth, the expression of fetal Aγ- and Gγ-globin ceases, and then adult β-globin is mostly expressed. It has been shown that in addition to erythroid cells, hemoglobin is widely expressed in nonerythroid cells including neurons of the cortex, hippocampus, and cerebellum in rodents; embryonic and adult brain neurons in mice; and mesencephalic dopaminergic brain cells in humans, mice, and rats. Lately, there is growing evidence that different forms of anemia (changes in the number and quality of blood cells) may be involved in (or may accompany) the pathogenesis of various cognitive and mental disorders, such as Alzheimer’s and Parkinson’s diseases, depression of various severity levels, bipolar disorders, and schizophrenia. Higher hemoglobin concentrations in the blood may lead to hyperviscosity, hypovolemia, and lung diseases, which may cause brain hypoxia and anomalies of brain function, which may also result in cognitive deficits. Methods: In this study, a search for unannotated single-nucleotide polymorphisms (SNPs) of erythroid genes was initially performed using our previously created and published SNP-TATA_Z-tester, which is a Web service for computational analysis of a given SNP for in silico estimation of its influence on the affinity of TATA-binding protein (TBP) for TATA and TATA-like sequences. The obtained predictions were finally verified in vitro by an electrophoretic mobility shift assay (EMSA). Results: On the basis of these experimental in vitro results and literature data, we studied TATA box SNPs influencing both human erythropoiesis and cognitive abilities. For instance, TBP–TATA affinity in the HbZ promoter decreases 6.6-fold as a result of a substitution in the TATA box (rs113180943), thereby possibly disrupting stage-dependent events of “switching” of hemoglobin genes and thus causing erythroblastosis. Therefore, rs113180943 may be a candidate marker of severe hemoglobinopathies with comorbid cognitive and mental disorders associated with cerebral blood flow disturbances. Conclusions: The literature data and experimental and computations results suggest that the uncovered candidate SNP markers of erythropoiesis anomalies may also be studied in cohorts of patients with cognitive and/or mental disorders with comorbid erythropoiesis diseases in comparison to conventionally healthy volunteers. Research into the regulatory mechanisms by which the identified SNP markers contribute to the development of hemoglobinopathies and of the associated cognitive deficits will allow physicians not only to take timely and adequate measures against hemoglobinopathies but also to implement strategies preventing cognitive and mental disorders.