also: ひぞうっこ
noun
favorite child; favorite student; apple of one's eye
Refers to a person (often a child, student, or protégé) who is cherished and specially favored by a parent, teacher, or mentor. Conveys warmth and affection.
彼は社長の秘蔵っ子として、重要なプロジェクトを任されている。
As the president's favorite protégé, he is entrusted with important projects.
あの子は先生の秘蔵っ子で、いつも特別扱いされている。
That child is the teacher's favorite and always gets special treatment.
お気に入り is a general term for a favorite thing or person, while 秘蔵っ子 specifically refers to a cherished person (child, student, protégé) and carries a stronger nuance of being treasured and protected.
愛弟子 is a beloved disciple or pupil, often in traditional arts or crafts. 秘蔵っ子 is broader and can refer to any favored child or junior, not necessarily a formal disciple.
Compound of 秘蔵 (ひぞう, 'treasuring, cherishing') + っ子 (っこ, a suffix meaning 'child' or 'person'). The suffix っ子 is a colloquial variant of 子 (こ). The reading ひぞっこ is a contraction of ひぞうっこ.