-따라

Attached to a time word such as 오늘 or 그날, it means 'on that day of all days, unusually then': something differs from the usual, often inconveniently.

조사Particles

Han: The 'of all days' particle 따라 attaches directly to the time word; 에 따라 means 'according to'.

Examples

하필 그날따라 휴대폰을 집에 두고 나와서 연락을 못 받았어요.That day of all days I'd left my phone at home, so I missed the call.

오늘따라 출근길이 유난히 길게 느껴졌다.My commute felt unusually long today, for some reason.

평소에는 조용하던 아이가 그날따라 이상하게 말이 많았다.The usually quiet child was strangely talkative that day.

-따라vs-에 따라에 따라 means 'depending on, according to'; 따라 is 'of all days': 날씨에 따라 일정이 바뀔 수 있어요 vs 오늘따라 날씨가 유난히 춥네요.

N (time: 오늘, 그날, 이날)+따라

오늘 → 오늘따라; 그날 → 그날따라; 이날 → 이날따라

It is a particle written attached to the noun, with no 에: 오늘따라, not 오늘에 따라. It combines mainly with a few time words: 오늘, 그날, 이날.
The sentence describes something unlike the usual: 유난히, 왠지, 이상하게, 하필 often appear with it.
It is not the verb 따르다 'to follow': N에 따라 means 'according to N' and needs 에.

Wrong: ~~오늘에 따라 길이 유난히 많이 막혀요.~~

Right: 오늘따라 길이 유난히 많이 막혀요.

The 'of all days' particle 따라 attaches directly to the time word; 에 따라 means 'according to'.

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