Postgres 11

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create table t (id int, pid int , name name , dt date) partition by range(dt);
--create unique index on t(id,pid);
--alter table t  add constraint uk unique  (id);

CREATE TABLE

--create unique index on t(id,pid);
alter table t  add constraint uk unique  (id,pid,dt);

ALTER TABLE

create table t1 partition of t for values from ('2020-01-01') to ('2020-02-01');
alter table t1  add constraint uk1 unique  (id,pid);
create table t2 partition of t for values from ('2020-02-01') to ('2020-03-01');
alter table t2  add constraint uk2 unique  (id,pid);
create table t4 partition of t for values from ('2020-03-01') to ('2020-04-01');
alter table t4  add constraint uk3 unique  (id,pid);
create table t3 partition of t for values from ('2020-04-01') to ('2020-05-01');
alter table t3  add constraint uk4 unique  (id,pid);

CREATE TABLE

ALTER TABLE

CREATE TABLE

ALTER TABLE

CREATE TABLE

ALTER TABLE

CREATE TABLE

ALTER TABLE

insert into t(id,pid,name,dt) values (1,2,'raj','2020-01-01')
on conflict (id,pid) do nothing;

ERROR:  there is no unique or exclusion constraint matching the ON CONFLICT specification