mRNA vaccines are aimed at enabling a human immune system to combat the virus and do not do anything to the DNA of a human cell.
It would seem that those who post such claims misunderstand genetics. The Pfizer COVID-19 vaccine is an mRNA vaccine (or messenger RNA vaccine). According to the PHG Foundation, a health policy think tank, RNA vaccines work by introducing an mRNA sequence (the molecule that tells cells what to build) coded for a disease-specific antigen. Once produced within the body, the immune system recognizes the antigen, preparing it to fight the real thing.
There are many advantages to mRNA vaccines, including the fact that they can be quick and cheap to develop. Real concerns center on the length of protection they offer and not on whether they alter your DNA. Indeed, mRNA vaccines do not alter or modify the DNA in a human cell. They are designed to trigger an immune response by instructing the body's cells to produce the vaccine antigens.
The COVID-19 pandemic has given rise to a lot of potentially dangerous misinformation. For reliable advice on COVID-19, including symptoms, prevention, and available treatment, please refer to the World Health Organization or your national healthcare authority.