This is the 5837th most frequent Korean word.
부친이
"부친이" means "father is" or "father" (subject marker).
In this context, '부친이' is the subject which specifies that the speaker's father performed the action of sending a letter.
부친이 편지를 보내셨습니다.
My father sent a letter.
This usage denotes '부친이' as the formal subject, indicating the event involving the speaker's father.
내 부친이 오늘 모임에 오십니다.
My father is coming to the meeting today.
Here, '부친이' is the subject of the sentence and refers to 'my father' in a formal and respectful tone.