Dependent question

When looking at your filed tax return in the dependent box , do all children in this box count as a dependent even if the child tax credit box is not checked ? 

My ex and I claim every other year , my return was rejected because he claimed but he swears he did not . He showed me his return and it DOES have our sons name but the box on the right is checked (credit for other dependents) and not the box on the left . 

the years that I do not claim my son he does not even show up in the dependent box he shows up in the filing status under my HOH section 

I hope this makes sense , thank you !