The human X-linked zinc finger MYM-type protein 3 (ZMYM3) contains the longest GA-STR identified across protein-coding gene 5' UTR sequences, at 32-repeats. This exceptionally long GA-STR is located at a complex string of GA-STRs with a human-specific formula across the complex as follows: (GA)8-(GA)4-(GA)6-(GA)32 (ZMYM3-207 ENST00000373998.5). ZMYM3 was previously reported among the top three genes involved in the progression of late-onset Alzheimer's disease. Here we sequenced the ZMYM3 GA-STR complex in 750 human male subjects, consisting of late-onset neurocognitive disorder (NCD) as a clinical entity (n = 268) and matched controls (n = 482). We detected strict monomorphism of the GA-STR complex, except of the exceptionally long STR, which was architecturally skewed in respect of allele distribution between the NCD cases and controls [F (1, 50) = 12.283; p = 0.001]. Moreover, extreme alleles of this STR at 17, 20, 42, and 43 repeats were detected in seven NCD patients and not in the control group (Mid-P exact = 0.0003). A number of these alleles overlapped with alleles previously found in schizophrenia and bipolar disorder patients. In conclusion, we propose selective advantage for the exceptional length of the ZMYM3 GA-STR in human, and its link to a spectrum of diseases in which major cognition impairment is a predominant phenotype.