How to query for null values in json field type postgresql?

you can use the fact that elem->'occupation2' returns string null of type json, so your query will be:

select
    *
from  json_array_elements(
  '[{"name": "Toby", "occupation": "Software Engineer"},
    {"name": "Zaphod", "occupation": "Galactic President"} ,
    {"name2": "Zaphod", "occupation2": null} ]'
) as elem
where (elem->'occupation2')::text="null"

{"name2": "Zaphod", "occupation2": null}

If you want to get all elements where value is null in JSON or key doesn’t exists, you can just do:

select
    *
from  json_array_elements(
  '[{"name": "Toby", "occupation": "Software Engineer"},
    {"name": "Zaphod", "occupation": "Galactic President"} ,
    {"name2": "Zaphod", "occupation2": null} ]'
) as elem
where (elem->>'occupation2') is null

{"name": "Toby", "occupation": "Software Engineer"}
{"name": "Zaphod", "occupation": "Galactic President"}
{"name2": "Zaphod", "occupation2": null}

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