First of all, kudos to you for looking out for the emotional and spiritual good of your son, even if money is tight.
Most Yeshiva high schools charge about 10 – 15 thousand dollars for tuition. (This is not so that they can make exorbitant profits – it just costs a lot to run a school.) However, my impression is that most schools will settle for between 4 – 6 thousand in a case of legitimate financial need. However, if you’d like people to list specific schools where they think this might be the case, it might be a good idea to try to describe what type of background your son is coming from and what type of school he’d like to attend.