I use PostgreSQL 10 and I run CREATE EXTENSION unaccent; succesfully. I have a plgsql function that contains the following
whereText := 'lower(unaccent(place.name)) LIKE lower(unaccent($1))';
later, according to what user chose, more clauses may be added to the whereText. 
The whereText is finally used in the query:
placewithkeys := '%'||placename||'%';
RETURN QUERY EXECUTE format('SELECT id, name FROM '||fromText||' WHERE '||whereText)
     USING  placewithkeys , event, date;
The whereText := 'LOWER(unaccent(place.name)) LIKE LOWER(unaccent($1))'; does not work, even if I remove the LOWER part. 
I do select __my_function('Τζι'); and I get nothing back, even though I should get  back results, because in the database there is the name Τζίμα
If I remove the unaccent and leave the LOWER it works, but not for accents : τζ brings Τζίμα back as it should. It seems like the unaccent is causing a problem. 
What am I missing? How can I fix this?
Since there were comments about the syntax and possible SQLi , I provide the whole function definition, now changed to work accent-insensitive and case-insensitive in Greek:
CREATE  FUNCTION __a_search_place
(placename text, eventtype integer, eventdate integer, eventcentury integer, constructiondate integer, constructioncentury integer, arstyle integer, artype integer)
RETURNS TABLE
(place_id bigint, place_name text, place_geom geometry) 
AS $$
DECLARE
selectText text;
fromText text;
whereText text;
usingText text; 
placewithkeys text;
BEGIN   
    fromText := '
    place
    JOIN cep ON place.id = cep.place_id
    JOIN event ON cep.event_id = event.id                     
    ';  
    whereText := 'unaccent(place.name) iLIKE  unaccent($1)';   
    placewithkeys := '%'||placename||'%';
    IF constructiondate IS NOT NULL OR constructioncentury IS NOT NULL OR arstyle IS NOT NULL OR artype IS NOT NULL THEN
        fromText := fromText || '
        JOIN construction ON cep.construction_id = construction.id
        JOIN construction_atype ON construction.id = construction_atype.construction_id
        JOIN construction_astyle ON construction.id = construction_astyle.construction_id
        JOIN atype ON atype.id = construction_atype.atype_id
        JOIN astyle ON astyle.id = construction_astyle.astyle_id  
        ';   
    END IF;    
    IF eventtype IS NOT NULL THEN
        whereText := whereText || 'AND event.type = $2 ';
    END IF;
    IF eventdate IS NOT NULL THEN
        whereText := whereText || 'AND event.date = $3 ';
    END IF;
    IF eventcentury IS NOT NULL THEN
        whereText := whereText || 'AND event.century = $4 ';
    END IF;    
    IF constructiondate IS NOT NULL THEN
        whereText := whereText || 'AND construction.date = $5 ';
    END IF;
    IF constructioncentury IS NOT NULL THEN
        whereText := whereText || 'AND construction.century = $6 ';
    END IF;
    IF arstyle IS NOT NULL THEN
        whereText := whereText || 'AND astyle.id = $7 ';
    END IF;
    IF artype IS NOT NULL THEN
        whereText := whereText || 'AND atype.id = $8 ';
    END IF;   
    whereText := whereText || '    
    GROUP BY place.id, place.geom, place.name
    ';    
    RETURN QUERY EXECUTE format('SELECT place.id, place.name, place.geom FROM '||fromText||' WHERE '||whereText)      
    USING  placewithkeys, eventtype, eventdate, eventcentury, constructiondate, constructioncentury, arstyle, artype ;
END;
$$
LANGUAGE plpgsql;