Dear N.T. Markad, I don't know which kind of fermentation your speak about, maybe you refer to anaerobic fermentation which is part of the SSF, generating methane. There are many species of methanogenic microorganisms involved in anaerobic decomposition of organic fraction. They use various organic substrates as an energy source for their metabolism (for generating methane but also for cells growth), some of them use hydrogen, CO2, formate, acetate but one of the species (Methanosacina barkeri, that is frequently found in anaerobic microbiota, in mesophilic temperature regime) uses methanol as energy source. By enriching the substrate with methanol, the growth of this much „diligent, productive” specie is supported, therefore the methane yield is higher.
Just to add, the addition of methanol is to sterilize or inoculate the media. As stated, methanol also promotes the growth of proteins and other species that aid the process of fermentation. There are quite a number of studies in literature that explain this practice in detail.
Thanks for details, this is indeed a different research topic. I indicate you 2 papers that might help in finding the answer. There is stated that methanol can stimulate citric acid fermentation but there are controversial findings as well: