A PostgreSQL quine adapted from this ANSI SQL quine (works for PostgreSQL 11.15):
SELECT left(A.v, 81) || chr(39) || A.v || chr(39) || right(A.v, 12) FROM (SELECT 'SELECT left(A.v, 81) || chr(39) || A.v || chr(39) || right(A.v, 12) FROM (SELECT AS v) AS A;' AS v) AS A;