Returning a json array slice in PostgreSQL

select  array_to_json 
           (select  array_agg(my_db_field->n order by n) 
            from    generate_series(0,least(300,json_array_length(my_db_field))-1) gs(n) 

from    my_db_table

This solution (the original in this answer) most likely does not guarantee the order of the elements

select (array(select json_array_elements(my_db_field)))[1:300]
from    my_db_table

In PostgreSQL 12, you can obtain JSONB array slice using the jsonb_path_query_array function:

SELECT jsonb_path_query_array('["a","b","c","d","e","f"]', '$[2 to 4]');
 ["c", "d", "e"]
(1 row)