diff --git a/src/metric-engine/src/engine/create.rs b/src/metric-engine/src/engine/create.rs
index b8b39a11ddf6..0ff5bb75f8a2 100644
--- a/src/metric-engine/src/engine/create.rs
+++ b/src/metric-engine/src/engine/create.rs
@@ -405,6 +405,7 @@ impl MetricEngineInner {
         request: &RegionCreateRequest,
     ) -> RegionCreateRequest {
         let mut data_region_request = request.clone();
+        let mut primary_key = vec![ReservedColumnId::table_id(), ReservedColumnId::tsid()];
 
         // concat region dir
         data_region_request.region_dir = join_dir(&request.region_dir, DATA_REGION_SUBDIR);
@@ -416,6 +417,7 @@ impl MetricEngineInner {
             .for_each(|metadata| {
                 if metadata.semantic_type == SemanticType::Tag {
                     metadata.column_schema.set_nullable();
+                    primary_key.push(metadata.column_id);
                 }
             });
 
@@ -423,8 +425,7 @@ impl MetricEngineInner {
         let [table_id_col, tsid_col] = Self::internal_column_metadata();
         data_region_request.column_metadatas.push(table_id_col);
         data_region_request.column_metadatas.push(tsid_col);
-        data_region_request.primary_key =
-            vec![ReservedColumnId::table_id(), ReservedColumnId::tsid()];
+        data_region_request.primary_key = primary_key;
 
         // set index options
         set_index_options_for_data_region(&mut data_region_request.options);
@@ -608,7 +609,7 @@ mod test {
         assert_eq!(data_region_request.column_metadatas.len(), 4);
         assert_eq!(
             data_region_request.primary_key,
-            vec![ReservedColumnId::table_id(), ReservedColumnId::tsid()]
+            vec![ReservedColumnId::table_id(), ReservedColumnId::tsid(), 1]
         );
     }
 }
diff --git a/tests/cases/standalone/common/create/create_metric_table.result b/tests/cases/standalone/common/create/create_metric_table.result
index 0a153ec733fc..5256f9d1b91b 100644
--- a/tests/cases/standalone/common/create/create_metric_table.result
+++ b/tests/cases/standalone/common/create/create_metric_table.result
@@ -84,3 +84,65 @@ DROP TABLE phy;
 
 Affected Rows: 0
 
+-- create one with other primary keys
+CREATE TABLE phy2 (ts timestamp time index, val double, abc string, def string, primary key (abc, def)) engine=metric with ("physical_metric_table" = "");
+
+Affected Rows: 0
+
+DESC TABLE phy2;
+
++--------+----------------------+-----+------+---------+---------------+
+| Column | Type                 | Key | Null | Default | Semantic Type |
++--------+----------------------+-----+------+---------+---------------+
+| ts     | TimestampMillisecond | PRI | NO   |         | TIMESTAMP     |
+| val    | Float64              |     | YES  |         | FIELD         |
+| abc    | String               | PRI | YES  |         | TAG           |
+| def    | String               | PRI | YES  |         | TAG           |
++--------+----------------------+-----+------+---------+---------------+
+
+DROP TABLE phy2;
+
+Affected Rows: 0
+
+-- fuzz test case https://github.com/GreptimeTeam/greptimedb/issues/3612
+CREATE TABLE `auT`(
+  incidunt TIMESTAMP(3) TIME INDEX,
+  `QuaErAT` BOOLEAN,
+  `REPREHenDERIt` BOOLEAN DEFAULT true,
+  `Et` INT NULL,
+  `AutEM` INT,
+  esse DOUBLE,
+  `Tempore` BOOLEAN,
+  `reruM` BOOLEAN,
+  `eRrOR` BOOLEAN NULL,
+  `cOMmodi` BOOLEAN,
+  `PERfERENdIS` DOUBLE,
+  `eSt` FLOAT DEFAULT 0.70978713,
+  PRIMARY KEY(`cOMmodi`, `PERfERENdIS`, esse)
+) ENGINE = metric with ("physical_metric_table" = "");
+
+Affected Rows: 0
+
+DESC TABLE `auT`;
+
++---------------+----------------------+-----+------+------------+---------------+
+| Column        | Type                 | Key | Null | Default    | Semantic Type |
++---------------+----------------------+-----+------+------------+---------------+
+| incidunt      | TimestampMillisecond | PRI | NO   |            | TIMESTAMP     |
+| QuaErAT       | Boolean              |     | YES  |            | FIELD         |
+| REPREHenDERIt | Boolean              |     | YES  | true       | FIELD         |
+| Et            | Int32                |     | YES  |            | FIELD         |
+| AutEM         | Int32                |     | YES  |            | FIELD         |
+| esse          | Float64              | PRI | YES  |            | TAG           |
+| Tempore       | Boolean              |     | YES  |            | FIELD         |
+| reruM         | Boolean              |     | YES  |            | FIELD         |
+| eRrOR         | Boolean              |     | YES  |            | FIELD         |
+| cOMmodi       | Boolean              | PRI | YES  |            | TAG           |
+| PERfERENdIS   | Float64              | PRI | YES  |            | TAG           |
+| eSt           | Float32              |     | YES  | 0.70978713 | FIELD         |
++---------------+----------------------+-----+------+------------+---------------+
+
+DROP TABLE `auT`;
+
+Affected Rows: 0
+
diff --git a/tests/cases/standalone/common/create/create_metric_table.sql b/tests/cases/standalone/common/create/create_metric_table.sql
index fcc41ff11541..a5be70c95502 100644
--- a/tests/cases/standalone/common/create/create_metric_table.sql
+++ b/tests/cases/standalone/common/create/create_metric_table.sql
@@ -23,3 +23,31 @@ DROP TABLE t1;
 DROP TABLE t2;
 
 DROP TABLE phy;
+
+-- create one with other primary keys
+CREATE TABLE phy2 (ts timestamp time index, val double, abc string, def string, primary key (abc, def)) engine=metric with ("physical_metric_table" = "");
+
+DESC TABLE phy2;
+
+DROP TABLE phy2;
+
+-- fuzz test case https://github.com/GreptimeTeam/greptimedb/issues/3612
+CREATE TABLE `auT`(
+  incidunt TIMESTAMP(3) TIME INDEX,
+  `QuaErAT` BOOLEAN,
+  `REPREHenDERIt` BOOLEAN DEFAULT true,
+  `Et` INT NULL,
+  `AutEM` INT,
+  esse DOUBLE,
+  `Tempore` BOOLEAN,
+  `reruM` BOOLEAN,
+  `eRrOR` BOOLEAN NULL,
+  `cOMmodi` BOOLEAN,
+  `PERfERENdIS` DOUBLE,
+  `eSt` FLOAT DEFAULT 0.70978713,
+  PRIMARY KEY(`cOMmodi`, `PERfERENdIS`, esse)
+) ENGINE = metric with ("physical_metric_table" = "");
+
+DESC TABLE `auT`;
+
+DROP TABLE `auT`;