A countertop extends into a doorway between our kitchen and living. Should we put up a mezuzah and, if so, where?

From the description and picture, I can’t tell which side is the (Halachic) right-hand side, so I’m assuming that you already have that figured out.

If the right-hand side is the straight (“normal”) side, then the Mezuzah should be attached as usual. This is provided that the cabinets there are not flush with the “doorpost”. If they are flush, it would be exempt.

If the side with the counter is the right-hand side (and assuming that the counter has a height of at least 31.6 inches [80 centimeters]), the Mezuzah should be attached to the top third of the side of the counter-top (meaning, the lower wall under the counter-top which protrudes into the doorway – as opposed to the actual doorway above the counter).

No Bracha is recited.

Sources:

ראה: פתחי תשובה ביו”ד סי’ רפ”ו ס”ק י’ בשם סידור דרך חיים (ליסא), וכ”ה בקיצוש”ע סי’ י”א סעי’ י”ב, מקדש מעט סי’ רפ”ו ס”ק ל”ו, חובת הדר ח”ב פ”ח ס”ק ו-ז, ועוד.

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