（在）…之餘grammar point · tier 1 · in the margin beside X (（在）…之餘 — in the spare room alongside the main activity, also do Y)
In the spare room left over beside a main activity: X is the bulk of what one does, and Y happens in the margin alongside it.
字源 FORM what the parts do
餘 is food (食, 飠) with 余 lent only for the sound yú; it carries surplus, what is left over. 之 is the classical of, tying the main activity to its 餘. 在 may open the bracket to set you down inside that leftover stretch. The main activity fills the slot before 之餘; what spills into its margin comes after.
故事 STORY a scene to remember it by
The main dish fills the plate, and a strip of the table is still bare beside it; the second thing is set down on that bare strip.
字源記憶法
框 · Frame
（在）[main activity X] 之餘，[subject] [also does Y]
觸 · Trigger
You want to name a main activity and say that a second thing fits into the spare time or energy left over beside it.
序 · The move
1Put the main, larger activity in the slot before 之餘 (optionally opened with 在).Is the thing before 之餘 the bulk of what the subject does — the plate, not the bare strip?
2Write the second clause for what happens in the margin, often led by 還/也.Does the second thing fit into the leftover room beside the main activity, not replace it or run at the same scale?
3Keep it to written/formal register.之餘 reads written; spoken Mandarin would reach for 的時候 or 同時 instead.
例 · Examples
1他在in (the margin of)工作work — the main activity之餘in what is left over beside it，還still, on top of that不忘does not forget to充實enrich, build up自己的專業知識professional knowledge。
Alongside his work, he still does not forget to build up his own professional knowledge.
界 · Boundary
（在）…的時候
之餘 frames the second thing as fitting into the spare margin left over beside the main activity (the bulk is X; Y squeezes into the rest). 的時候 only times Y to overlap X, with no claim that one is the bulk and the other the leftover. 之餘 reads written; 的時候 is the everyday choice.
一邊…一邊…
一邊…一邊… runs two activities at full scale at the same moment, side by side. 之餘 makes one the main bulk and slots the other into its leftover room, not co-equal and not necessarily simultaneous.
他工作之餘 ✗ → 他在工作之餘 / 他工作之餘 ✓ (在 is optional; either opens the bracket, but the main activity must sit before 之餘, never after)
他在充實專業知識之餘，還工作。 ✗ → 他在工作之餘，還充實專業知識。 ✓ (the bulk activity goes before 之餘; the margin-filler comes after — reversing them puts the small thing as the bulk)
他在工作之餘的時候充實知識。 ✗ → 他在工作之餘，充實知識。 ✓ (之餘 already frames the leftover stretch; stacking 的時候 on it doubles the framing)
English 'in his spare time' or 'besides working' floats freely as one phrase; Mandarin fixes the main activity before 之餘 and leans the second clause (often 還/也) on what fills the margin, and keeps the whole frame written rather than spoken.