Alzheimer’s disease (AD) is characterized by the presence of neuropsychiatric or behavioral and psychological symptoms of dementia (BPSD). BPSD have been associated with the APOE_ε4 allele, which is also the major genetic AD risk factor. Although the involvement of some circadian genes and orexin receptors in sleep and behavioral disorders has been studied in some psychiatric pathologies, including AD, there are no studies considering gene–gene interactions. The associations of one variant in PER2, two in PER3, two in OX2R and two in APOE were evaluated in 31 AD patients and 31 cognitively healthy subjects. Genotyping was performed using real-time PCR and capillary electrophoresis from blood samples. The allelic-genotypic frequencies of variants were calculated for the sample study. We explored associations between allelic variants with BPSD in AD patients based on the NPI, PHQ-9 and sleeping disorders questionnaires. Our results showed that the APOE_ε4 allele is an AD risk variant (p = 0.03). The remaining genetic variants did not reveal significant differences between patients and controls. The PER3_rs228697 variant showed a nine-fold increased risk for circadian rhythm sleep–wake disorders in Mexican AD patients, and our gene–gene interaction analysis identified a novel interaction between PERIOD and APOE gene variants. These findings need to be further confirmed in larger samples.