How can you find a literal percent sign (%) in PostgreSQL using a LIKE query?

You can try like this:

SELECT * FROM my_table  WHERE my_column LIKE '%\%%' ESCAPE '\';

Format

 <like predicate> ::=
      <match value> [ NOT ] LIKE <pattern>
        [ ESCAPE <escape character> ]

 <match value> ::= <character value expression>

 <pattern> ::= <character value expression>

 <escape character> ::= <character value expression>