Is it permissible for me to take a public sector job designated for the children of those affected by the general amnesty, and would that be considered as taking away the right of another person who might be more qualified than me or more deserving of the position?

As long as the offer came from the state, and the interests and justice were taken into account, there is no harm in accepting it, and it is not considered an encroachment on the rights of others. However, if you are assigned a task that you cannot perform, then apologize for it and request work that you can carry out to the fullest.