there are better ways to do this, but heres what i'd do.
under most linux boxes you'll need to add entries under /etc/passwd & /etc/shadow to create an account. since the mysql user won't actually be logging in, don't bother to create a home directory. look at the two files for examples of users for the syntax.
to add the mysql group, add something like:
mysql❌110:
to /etc/group with 110 being a unique group id. use the group id you specify when creating the account in passwd & shadow.