Assuming a JSON array in a Postgres 9.4 jsonb column, this would do the job:
SELECT DISTINCT ON (doc->'s') doc
FROM (
SELECT '[
{
"id":1,
"s":"foo"
},
{
"id":2,
"s":"bar"
},
{
"id":3,
"s":"foo"
}]'::jsonb AS j
) t
, jsonb_array_elements(t.j) WITH ORDINALITY t1(doc, rn)
ORDER BY doc->'s', rn;
Or, unless s is a nested object, it's probably cheaper to fold on the text value instead of the jsonb (sub-)record. Just use the operator ->> instead of -> in this case. The result is the same:
doc
----------------------
'{"s": "bar", "id": 2}'
'{"s": "foo", "id": 1}'
Replace the subquery t with your actual table.
Key elements are jsonb_array_elements() (or json_array_elements()) in a LATERAL join with WITH ORDINALITY and then the Postgres-specific DISTINCT ON.
Related, with more explanation: