Searching in Array performance?

We have a table of

id|school_id|parent_ids

where parent_ids is an array of ids.

If we don’t have the school_id and only parent_id to search for, then the query will search through all the table rows in parent_ids array, there might be thousands of rows, and parent_id might actually be within just few of them.

Does using IN in query for the array column could be a performance barrier in this case?

EDIT

Here is the dump of table structure:

-- ----------------------------
-- Table structure for schools_messages
-- ----------------------------
DROP TABLE IF EXISTS "public"."schools_messages";
CREATE TABLE "public"."schools_messages" (
  "id" int4 NOT NULL DEFAULT nextval('schools_messages_id_seq'::regclass),
  "message" jsonb NOT NULL DEFAULT '[]'::jsonb,
  "details" jsonb NOT NULL DEFAULT '[]'::jsonb,
  "school_id" int4 NOT NULL,
  "created_at" timestamp(0),
  "updated_at" timestamp(0),
  "parents_ids" int4[] DEFAULT ARRAY[]::integer[]
)
;
ALTER TABLE "public"."schools_messages" OWNER TO "prod_schools";

-- ----------------------------
-- Primary Key structure for table schools_messages
-- ----------------------------
ALTER TABLE "public"."schools_messages" ADD CONSTRAINT "schools_messages_pkey" PRIMARY KEY ("id");

-- ----------------------------
-- Foreign Keys structure for table schools_messages
-- ----------------------------
ALTER TABLE "public"."schools_messages" ADD CONSTRAINT "schools_messages_school_id_foreign" FOREIGN KEY ("school_id") REFERENCES "public"."trk_schools" ("id") ON DELETE CASCADE ON UPDATE NO ACTION;

I agree with Jack that your schema needs help. But you can still do this. Here we do this with one index lookup, using two core extensions intarray and btree_gist

CREATE EXTENSION intarray;
CREATE EXTENSION btree_gist;

CREATE INDEX ON public.schools_messages
  USING gist(school_id, parents_ids gist__int_ops);

VACUUM ANALYZE public.schools_messages;

SELECT *
FROM public.schools_messages
WHERE school_id = 42
  OR parent_id @> ARRAY[42];