noun
favorite pupil; teacher's pet
Refers to a student who is especially favored or cherished by a teacher or master, often in traditional arts, crafts, or academic settings. Can carry a slightly affectionate or envious tone depending on context.
彼は師匠の愛弟子として、特別な指導を受けている。
As the master's favorite pupil, he receives special instruction.
あの子は先生の愛弟子で、いつも褒められ
That kid is the teacher's pet and is always being praised.
教え子 refers to a former student or someone one has taught, without the connotation of special favoritism.
Compound of 愛 (beloved) and 弟子 (pupil/disciple). The reading まな for 愛 is an archaic or literary reading, seen in words like 愛でる (めでる).