～所(ところ)にAt the time, When, While, Timing

～ところに・～ところへ and の間に both express the idea of 'while', but with different nuance. ～ところに／へ emphasizes a scene or moment into which something else happens, e.g. ゲームをしているところへ兄が部屋に入ってきた ('While I was playing a game, my brother entered the room.') の間に, by contrast, simply describes one event taking place during another, without emphasizing a specific situation or setting.

Both can express the meaning of 'as soon as (A), (B)', but with different usage and nuance. が早いか marks an action that is followed immediately by another, often sudden or dramatic, meaning ‘no sooner than,’ as in ドアを開けるが早いか、子どもが飛び出してきた ('No sooner had I opened the door than a child burst out.'). ～ところに・～ところへ describes another event occurring at a certain stage of an action, focusing on coincidence in time rather than instant reaction, as in 出かけようとしたところに電話がかかってきた ('Just as I was about to go out, I got a phone call.').

Both ついでに and ～ところに・～ところへ relate to timing, but from different angles. ついでに expresses performing a second action while it's convenient, e.g. '買い物のついでに郵便局に寄った' ('I stopped at the post office while shopping'). ～ところに・～ところへ focuses on when something happens, often unexpectedly, e.g. '出かけようとしたところに電話がかかってきた' ('Just as I was about to leave, the phone rang').

Both describe an interruption during an action, but with different focus. ～ところに・～ところへ highlights timing or the moment of interruption, e.g. 出かけようとしたところに電話がかかってきた ('Just as I was about to leave, the phone rang.') 最中に stresses that the action was in full progress, e.g. 晩ご飯を作っている最中に電話が鳴った ('The phone rang when I was right in the middle of making dinner.')

Both express something happening during an ongoing action, but differ in focus. Compared to ているあいだに, which states in a straightforward manner one thing happening in the middle of another thing, ～ところに・～ところへplaces more of a focus on the 'scene' or situation, and is therefore often used to express a surprising or disturbing event.

ているところだ conveys that an action is in progress at that moment, with the nuance that the speaker is occupied with it, e.g. ゲームをしているところだ ('I'm in the middle of playing a video game.'). In contrast, ～ところに・～ところへ describes something happening at the moment of another action, e.g. ゲームをしているところに母に呼ばれた ('I was called by my mother while I was in the middle of playing a game.').