Various lineages of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have contributed to prolongation of the coronavirus disease 2019 (COVID-19) pandemic. Several non-synonymous mutations in SARS-CoV-2 proteins have generated multiple SARS-CoV-2 variants. In our previous report, we have shown an evenly uneven distribution of unique protein variants of SARS-CoV-2 is geo-location or demography-specific. However, the correlation between the demographic transmutability of the SARS-CoV-2 infection and mutations in various proteins remains unknown due to hidden symmetry/asymmetry in the occurrence of mutations. This study tracked how these mutations are emerging in SARS-CoV-2 proteins in six model countries and globally. In a geo-location, considering the mutations having a frequency of detection of at least five hundred in each SARS-CoV-2 protein; we studied the country-wise percentage of invariant residues. Our data revealed that since October 2020, highly frequent mutations in SARS-CoV-2 have been observed mostly in the Open Reading Frames (ORF) 7b and ORF8, worldwide. No such highly frequent mutations in any of the SARS-CoV-2 proteins were found in the UK, India, and Brazil, which does not correlate with the degree of transmissibility of the virus in India and Brazil. However, we have found a signature that SARS-CoV-2 proteins were evolving at a higher rate, and considering global data, mutations are detected in the majority of the available amino acid locations. Fractal analysis of each protein’s normalized factor time series showed a periodically aperiodic emergence of dominant variants for SARS-CoV-2 protein mutations across different countries. It was noticed that certain high-frequency variants have emerged in the last couple of months, and thus the emerging SARS-CoV-2 strains are expected to contain prevalent mutations in ORF3a, membrane, and ORF8 proteins. In contrast to other beta-coronaviruses, SARS-CoV-2 variants have rapidly emerged based on demographically dependent mutations. Characterization of the periodically aperiodic nature of the demographic spread of SARS-CoV-2 variants in various countries can contribute to the identification of the origin of SARS-CoV-2.