〜てこのかた
ever since
Verb て-form + このかた
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てこのかた means "ever since", looking back over the whole period from a past event to now: 生まれてこのかた、病気をしたことがない, "I've never been ill in my life".
The second half is usually a continuing state or something that has never happened in all that time. It often comes with 一度も〜ない or ずっと.
It's a literary version of て以来 (N3) and てから. The feeling is weightier, like looking back over a long stretch of life. 生まれてこのかた, "since I was born", is by far the most common use.
Don't confuse it with この前, "the other day". このかた here means "since then, from this side".
Examples
生まれてこのかた、病気をしたことがない。
I've never been ill in my life.
日本に来てこのかた、一度も国に帰っていない。
I haven't been home once since I came to Japan.
社会人になってこのかた、休みらしい休みがない。
Ever since I started working, I haven't had a proper holiday.
彼と別れてこのかた、一度も連絡を取っていない。
I haven't been in touch with him once since we split up.
物心ついてこのかた、ずっとこの町に住んでいる。
I've lived in this town for as long as I can remember.