No.
The mRNA Covid vaccines do not alter your DNA.
PERIOD.
Could mRNA Vaccines Permanently Alter DNA? Recent Science Suggests They Might.
https://childrenshealthdefense.org/defender/science-mrna-vaccines-alter-dna/
Their key findings were as follows: SARS-CoV-2 RNAs “can be reverse transcribed in human cells,” “these DNA sequences can be integrated into the cell genome and subsequently be transcribed” (a phenomenon called “retro-integration”) — and there are viable cellular pathways to explain how this happens.