With the below commands, user's default search_path can be set.
postgres=# \c postgres user1
You are now connected to database "postgres" as user "user1".
postgres=> show search_path;
search_path
----------------
"$user",public
(1 row)
search_path
with alter user
command to append a new schema my_schema
postgres=> \c postgres postgres
You are now connected to database "postgres" as user "postgres".
postgres=# alter user user1 set search_path='my_schema, "$user", public';
ALTER ROLE
postgres=# \c postgres user1
Password for user user1:
You are now connected to database "postgres" as user "user1".
postgres=> show search_path;
search_path
-------------
my_schema, "$user", public
(1 row)
Alternative:
postgres=# set role user1;
postgres=# show search_path;
search_path
-------------
my_schema, "$user", public
(1 row)