Is it permissible to be appointed to a government position if the reason for it is that the mother works in the ministry which allocates a percentage of appointments to employees' children, and is there any doubt concerning the salary?

If you are able to perform the job and carry out the tasks assigned to you as required, then there is no blame upon you. There is also no blame in the ministry granting the children of employees priority in its jobs to encourage workers and similar reasons, provided that the individual is qualified for the work.