after main schooling, those with aptitudes are sponsored by the state to pursue education as a caste- this is one of few social modes of mobility. They specialize, and their children are part of that new caste, unless and until they fail the training themselves (for mages.) It is not granted retroactively to the parents of the new mage, and it is up to them if they want to support their family upon return. Caste specific education, otherwise, is up to the family, who may be part of a group of families sharing education responsibilities. Our Knight rose through schooling in combat, was sponsored to grant soldier caste, and when he exceeded those aptitudes, was taken to the capitol to squire for another knight. Baseline- the younger you complete your schooling, the more likely it is you will be sponsored.
a select few are chosen for their exceeding standards to serve the royals and high nobles- these ones are not allowed any contact with their families post education and socially die, taking on a new identity, and are assigned as children of their mentors. due to identity scouring ritual clothing, to the public, these mages appear as their own caste, hidden within the capitol and dispersed where need be. The small children are assumed to be kept out of sight, unless they show aptitude to serve early.