The following script creates the schema required to use Postgres as the JDBC store for clustering Quartz. This was tested on Quartz 2.2.1 in Postgres 9.1 and 9.3

quartz_jdbc_store.sql

CREATE TABLE qrtz_blob_triggers (
    trigger_name character varying(80) NOT NULL,
    trigger_group character varying(80) NOT NULL,
    blob_data text,
    sched_name character varying(120) DEFAULT 'TestScheduler'::character varying NOT NULL
);

CREATE TABLE qrtz_calendars (
    calendar_name character varying(80) NOT NULL,
    calendar text NOT NULL,
    sched_name character varying(120) DEFAULT 'TestScheduler'::character varying NOT NULL
);

CREATE TABLE qrtz_cron_triggers (
    trigger_name character varying(80) NOT NULL,
    trigger_group character varying(80) NOT NULL,
    cron_expression character varying(80) NOT NULL,
    time_zone_id character varying(80),
    sched_name character varying(120) DEFAULT 'TestScheduler'::character varying NOT NULL
);

CREATE TABLE qrtz_fired_triggers (
    entry_id character varying(95) NOT NULL,
    trigger_name character varying(80) NOT NULL,
    trigger_group character varying(80) NOT NULL,
    instance_name character varying(80) NOT NULL,
    fired_time bigint NOT NULL,
    priority integer NOT NULL,
    state character varying(16) NOT NULL,
    job_name character varying(80),
    job_group character varying(80),
    is_nonconcurrent boolean,
    is_update_data boolean,
    sched_name character varying(120) DEFAULT 'TestScheduler'::character varying NOT NULL,
    sched_time bigint NOT NULL,
    requests_recovery boolean
);

CREATE TABLE qrtz_job_details (
    job_name character varying(128) NOT NULL,
    job_group character varying(80) NOT NULL,
    description character varying(120),
    job_class_name character varying(200) NOT NULL,
    is_durable boolean,
    is_nonconcurrent boolean,
    is_update_data boolean,
    sched_name character varying(120) DEFAULT 'TestScheduler'::character varying NOT NULL,
    requests_recovery boolean,
    job_data bytea
);

CREATE TABLE qrtz_locks (
    lock_name character varying(40) NOT NULL,
    sched_name character varying(120) DEFAULT 'TestScheduler'::character varying NOT NULL
);

INSERT INTO QRTZ_LOCKS VALUES('trigger_access');
INSERT INTO QRTZ_LOCKS VALUES('job_access');
INSERT INTO QRTZ_LOCKS VALUES('calendar_access');
INSERT INTO QRTZ_LOCKS VALUES('state_access');
INSERT INTO QRTZ_LOCKS VALUES('misfire_access');

CREATE TABLE qrtz_paused_trigger_grps (
    trigger_group character varying(80) NOT NULL,
    sched_name character varying(120) DEFAULT 'TestScheduler'::character varying NOT NULL
);

CREATE TABLE qrtz_scheduler_state (
    instance_name character varying(200) NOT NULL,
    last_checkin_time bigint,
    checkin_interval bigint,
    sched_name character varying(120) DEFAULT 'TestScheduler'::character varying NOT NULL
);

CREATE TABLE qrtz_simple_triggers (
    trigger_name character varying(80) NOT NULL,
    trigger_group character varying(80) NOT NULL,
    repeat_count bigint NOT NULL,
    repeat_interval bigint NOT NULL,
    times_triggered bigint NOT NULL,
    sched_name character varying(120) DEFAULT 'TestScheduler'::character varying NOT NULL
);

CREATE TABLE qrtz_simprop_triggers (
    sched_name character varying(120) NOT NULL,
    trigger_name character varying(200) NOT NULL,
    trigger_group character varying(200) NOT NULL,
    str_prop_1 character varying(512),
    str_prop_2 character varying(512),
    str_prop_3 character varying(512),
    int_prop_1 integer,
    int_prop_2 integer,
    long_prop_1 bigint,
    long_prop_2 bigint,
    dec_prop_1 numeric(13,4),
    dec_prop_2 numeric(13,4),
    bool_prop_1 boolean,
    bool_prop_2 boolean
);

CREATE TABLE qrtz_triggers (
    trigger_name character varying(80) NOT NULL,
    trigger_group character varying(80) NOT NULL,
    job_name character varying(80) NOT NULL,
    job_group character varying(80) NOT NULL,
    description character varying(120),
    next_fire_time bigint,
    prev_fire_time bigint,
    priority integer,
    trigger_state character varying(16) NOT NULL,
    trigger_type character varying(8) NOT NULL,
    start_time bigint NOT NULL,
    end_time bigint,
    calendar_name character varying(80),
    misfire_instr smallint,
    job_data bytea,
    sched_name character varying(120) DEFAULT 'TestScheduler'::character varying NOT NULL
);


ALTER TABLE ONLY qrtz_blob_triggers
    ADD CONSTRAINT qrtz_blob_triggers_pkey PRIMARY KEY (sched_name, trigger_name, trigger_group);

ALTER TABLE ONLY qrtz_calendars
    ADD CONSTRAINT qrtz_calendars_pkey PRIMARY KEY (sched_name, calendar_name);

ALTER TABLE ONLY qrtz_cron_triggers
    ADD CONSTRAINT qrtz_cron_triggers_pkey PRIMARY KEY (sched_name, trigger_name, trigger_group);

ALTER TABLE ONLY qrtz_fired_triggers
    ADD CONSTRAINT qrtz_fired_triggers_pkey PRIMARY KEY (sched_name, entry_id);

ALTER TABLE ONLY qrtz_job_details
    ADD CONSTRAINT qrtz_job_details_pkey PRIMARY KEY (sched_name, job_name, job_group);

ALTER TABLE ONLY qrtz_locks
    ADD CONSTRAINT qrtz_locks_pkey PRIMARY KEY (sched_name, lock_name);

ALTER TABLE ONLY qrtz_paused_trigger_grps
    ADD CONSTRAINT qrtz_paused_trigger_grps_pkey PRIMARY KEY (sched_name, trigger_group);

ALTER TABLE ONLY qrtz_scheduler_state
    ADD CONSTRAINT qrtz_scheduler_state_pkey PRIMARY KEY (sched_name, instance_name);

ALTER TABLE ONLY qrtz_simple_triggers
    ADD CONSTRAINT qrtz_simple_triggers_pkey PRIMARY KEY (sched_name, trigger_name, trigger_group);

ALTER TABLE ONLY qrtz_simprop_triggers
    ADD CONSTRAINT qrtz_simprop_triggers_pkey PRIMARY KEY (sched_name, trigger_name, trigger_group);

ALTER TABLE ONLY qrtz_triggers
    ADD CONSTRAINT qrtz_triggers_pkey PRIMARY KEY (sched_name, trigger_name, trigger_group);

CREATE INDEX fki_qrtz_simple_triggers_job_details_name_group ON qrtz_triggers USING btree (job_name, job_group);

CREATE INDEX fki_qrtz_simple_triggers_qrtz_triggers ON qrtz_simple_triggers USING btree (trigger_name, trigger_group);

CREATE INDEX idx_qrtz_ft_j_g ON qrtz_fired_triggers USING btree (sched_name, job_name, job_group);

CREATE INDEX idx_qrtz_ft_jg ON qrtz_fired_triggers USING btree (sched_name, job_group);

CREATE INDEX idx_qrtz_ft_t_g ON qrtz_fired_triggers USING btree (sched_name, trigger_name, trigger_group);

CREATE INDEX idx_qrtz_ft_tg ON qrtz_fired_triggers USING btree (sched_name, trigger_group);

CREATE INDEX idx_qrtz_ft_trig_inst_name ON qrtz_fired_triggers USING btree (sched_name, instance_name);

CREATE INDEX idx_qrtz_j_grp ON qrtz_job_details USING btree (sched_name, job_group);

CREATE INDEX idx_qrtz_t_c ON qrtz_triggers USING btree (sched_name, calendar_name);

CREATE INDEX idx_qrtz_t_g ON qrtz_triggers USING btree (sched_name, trigger_group);

CREATE INDEX idx_qrtz_t_j ON qrtz_triggers USING btree (sched_name, job_name, job_group);

CREATE INDEX idx_qrtz_t_jg ON qrtz_triggers USING btree (sched_name, job_group);

CREATE INDEX idx_qrtz_t_n_g_state ON qrtz_triggers USING btree (sched_name, trigger_group, trigger_state);

CREATE INDEX idx_qrtz_t_n_state ON qrtz_triggers USING btree (sched_name, trigger_name, trigger_group, trigger_state);

CREATE INDEX idx_qrtz_t_next_fire_time ON qrtz_triggers USING btree (sched_name, next_fire_time);

CREATE INDEX idx_qrtz_t_nft_misfire ON qrtz_triggers USING btree (sched_name, misfire_instr, next_fire_time);

CREATE INDEX idx_qrtz_t_nft_st ON qrtz_triggers USING btree (sched_name, trigger_state, next_fire_time);

CREATE INDEX idx_qrtz_t_nft_st_misfire ON qrtz_triggers USING btree (sched_name, misfire_instr, next_fire_time, trigger_state);

CREATE INDEX idx_qrtz_t_nft_st_misfire_grp ON qrtz_triggers USING btree (sched_name, misfire_instr, next_fire_time, trigger_group, trigger_state);

CREATE INDEX idx_qrtz_t_state ON qrtz_triggers USING btree (sched_name, trigger_state);

ALTER TABLE ONLY qrtz_blob_triggers
    ADD CONSTRAINT qrtz_blob_triggers_sched_name_fkey FOREIGN KEY (sched_name, trigger_name, trigger_group) REFERENCES qrtz_triggers(sched_name, trigger_name, trigger_group);

ALTER TABLE ONLY qrtz_cron_triggers
    ADD CONSTRAINT qrtz_cron_triggers_sched_name_fkey FOREIGN KEY (sched_name, trigger_name, trigger_group) REFERENCES qrtz_triggers(sched_name, trigger_name, trigger_group);

ALTER TABLE ONLY qrtz_simple_triggers
    ADD CONSTRAINT qrtz_simple_triggers_sched_name_fkey FOREIGN KEY (sched_name, trigger_name, trigger_group) REFERENCES qrtz_triggers(sched_name, trigger_name, trigger_group);

ALTER TABLE ONLY qrtz_simprop_triggers
    ADD CONSTRAINT qrtz_simprop_triggers_sched_name_fkey FOREIGN KEY (sched_name, trigger_name, trigger_group) REFERENCES qrtz_triggers(sched_name, trigger_name, trigger_group);

ALTER TABLE ONLY qrtz_triggers
    ADD CONSTRAINT qrtz_triggers_sched_name_fkey FOREIGN KEY (sched_name, job_name, job_group) REFERENCES qrtz_job_details(sched_name, job_name, job_group);

Is there any configuration to specify schema under which these tables are created?

Please be aware that in the original download files from http://www.quartz-scheduler.org/downloads/ there is under docs/dbTables the original DDL commands for setting up the tables required for PostgreSQL support with Quartz scheduler.