diff --git a/lightning/backend/local.go b/lightning/backend/local.go
index 8c0aa6cc9..ba15ca382 100644
--- a/lightning/backend/local.go
+++ b/lightning/backend/local.go
@@ -614,60 +614,44 @@ func (local *local) readAndSplitIntoRange(engineFile *LocalFile, engineUUID uuid
 		return ranges
 	}
 	if tablecodec.IsIndexKey(firstKey) {
-		// index engine
-		tableID, startIndexID, _, err := tablecodec.DecodeKeyHead(firstKey)
-		if err != nil {
-			return nil, err
+		type tblIndexRange struct {
+			tblID    int64
+			indexID  int64
+			startKey []byte
+			endKey   []byte
 		}
-		tableID, endIndexID, _, err := tablecodec.DecodeKeyHead(lastKey)
-		if err != nil {
-			return nil, err
-		}
-		indexCount := (endIndexID - startIndexID) + 1
-
-		// each index has to split into n / indexCount ranges
-		indexRangeCount := (n + indexCount - 1) / indexCount
-		for i := startIndexID; i <= endIndexID; i++ {
-			k := tablecodec.EncodeTableIndexPrefix(tableID, i)
-			iter.SeekGE(k)
-			// get first key of index i
-			startKeyOfIndex := append([]byte{}, iter.Key()...)
-
-			k = tablecodec.EncodeTableIndexPrefix(tableID, i+1)
-			// get last key of index i
-			iter.SeekLT(k)
 
-			lastKeyOfIndex := append([]byte{}, iter.Key()...)
+		// for partitioned table, there will be multiple physical tables and each physical table contains multiple indices
+		indexRanges := make([]*tblIndexRange, 0)
+		iter.First()
+		for iter.Valid() {
+			startKey := append([]byte{}, iter.Key()...)
 
-			_, startIndexID, _, err := tablecodec.DecodeKeyHead(startKeyOfIndex)
-			if err != nil {
-				return nil, err
-			}
-			_, endIndexID, _, err := tablecodec.DecodeKeyHead(lastKeyOfIndex)
+			tableID, indexID, _, err := tablecodec.DecodeKeyHead(startKey)
 			if err != nil {
 				return nil, err
 			}
 
-			if startIndexID != endIndexID {
-				// this shouldn't happen
-				log.L().DPanic("index ID not match",
-					zap.Int64("startID", startIndexID), zap.Int64("endID", endIndexID))
-				return nil, errors.New("index ID not match")
-			}
+			k := tablecodec.EncodeTableIndexPrefix(tableID, indexID+1)
+			iter.SeekLT(k)
+
+			endKey := append([]byte{}, iter.Key()...)
+			indexRanges = append(indexRanges, &tblIndexRange{tableID, indexID, startKey, endKey})
+			log.L().Debug("index key range", zap.Int64("tableID", tableID), zap.Int64("index", indexID),
+				zap.Binary("startKey", startKey), zap.Binary("endKey", endKey))
 
-			// if index is Unique or Primary, the key is encoded as
-			// tablePrefix{tableID}_indexPrefixSep{indexID}_indexedColumnsValue
-			// if index is non-Unique, key is encoded as
-			// tablePrefix{tableID}_indexPrefixSep{indexID}_indexedColumnsValue_rowID
+			iter.Next()
+		}
 
-			// we can split by indexColumnsValue to get indexRangeCount ranges from above Keys
+		indexRangeCount := (int(n) + len(indexRanges)) / len(indexRanges)
 
-			log.L().Info("split index to range",
-				zap.Int64("indexID", i), zap.Int64("rangeCount", indexRangeCount),
-				zap.Binary("start", startKeyOfIndex), zap.Binary("end", lastKeyOfIndex))
+		log.L().Info("split table index kv to range",
+			zap.Int("total index count", len(indexRanges)), zap.Int64("ranges", n),
+			zap.Int("index range count", indexRangeCount))
 
-			values := engineFile.splitValuesToRange(startKeyOfIndex, nextKey(lastKeyOfIndex), indexRangeCount, int(indexCount))
-			ranges = appendRanges(ranges, startKeyOfIndex, values)
+		for _, indexRange := range indexRanges {
+			values := engineFile.splitValuesToRange(indexRange.startKey, nextKey(indexRange.endKey), int64(indexRangeCount), len(indexRanges))
+			ranges = appendRanges(ranges, indexRange.startKey, values)
 		}
 	} else {
 		// data engine, we split keys by sample keys instead of by handle
diff --git a/tests/common_handle/run.sh b/tests/common_handle/run.sh
index e66be5c3c..101689f5d 100644
--- a/tests/common_handle/run.sh
+++ b/tests/common_handle/run.sh
@@ -16,7 +16,7 @@
 check_cluster_version 4 0 0 'local backend' || exit 0
 
 # enable cluster index
-run_sql 'set @@global.tidb_enable_clustered_index = 1' || (echo "tidb does not support cluster index yet, skip this test!" && exit 0)
+run_sql 'set @@global.tidb_enable_clustered_index = 1' || exit 0
 # wait for global variable cache invalid
 sleep 2
 
diff --git a/tests/parquet/run.sh b/tests/parquet/run.sh
index 691238b5a..6809612e9 100755
--- a/tests/parquet/run.sh
+++ b/tests/parquet/run.sh
@@ -21,6 +21,9 @@ check_row_count() {
 }
 
 for BACKEND in local importer tidb; do
+    if [ "$BACKEND" = 'local' ]; then
+        check_cluster_version 4 0 0 'local backend' || continue
+    fi
     run_sql 'DROP DATABASE IF EXISTS test'
     run_sql 'CREATE DATABASE test'
     run_sql -D test "source tests/$TEST_NAME/db.sql;"
diff --git a/tests/partitioned-table/config.toml b/tests/partitioned-table/config.toml
index e69de29bb..230b10175 100644
--- a/tests/partitioned-table/config.toml
+++ b/tests/partitioned-table/config.toml
@@ -0,0 +1,2 @@
+[tikv-importer]
+region-split-size = 50
diff --git a/tests/partitioned-table/data/partitioned.a-schema.sql b/tests/partitioned-table/data/partitioned.a-schema.sql
index 5c1a33a18..a67f4ec1b 100644
--- a/tests/partitioned-table/data/partitioned.a-schema.sql
+++ b/tests/partitioned-table/data/partitioned.a-schema.sql
@@ -1 +1 @@
-create table a (a int) partition by hash(a) partitions 5;
+create table a (a int, b varchar(16), KEY key_b (`b`)) partition by hash(a) partitions 5;
diff --git a/tests/partitioned-table/data/partitioned.a.sql b/tests/partitioned-table/data/partitioned.a.sql
index 23786b356..5961519a6 100644
--- a/tests/partitioned-table/data/partitioned.a.sql
+++ b/tests/partitioned-table/data/partitioned.a.sql
@@ -1,2 +1,10 @@
-insert into a values (268435456), (1), (262144), (32), (4), (65536), (8388608);
+insert into a values
+    (268435456, '268435456'),
+    (1, 'adgagdadgagag'),
+    (262144, 'gadgagaha'),
+    (32, '32'),
+    (4, 'hahaha'),
+    (65536, 'luck dog'),
+    (8388608, 'heyhey'),
+    (0, '999');
 
diff --git a/tests/partitioned-table/run.sh b/tests/partitioned-table/run.sh
index f1990fac3..be207e2c9 100755
--- a/tests/partitioned-table/run.sh
+++ b/tests/partitioned-table/run.sh
@@ -17,13 +17,19 @@
 
 set -eu
 
-run_sql 'DROP DATABASE IF EXISTS partitioned;'
+for BACKEND in tidb importer local; do
+    if [ "$BACKEND" = 'local' ]; then
+      check_cluster_version 4 0 0 'local backend' || continue
+    fi
 
-run_lightning
+    run_sql 'DROP DATABASE IF EXISTS partitioned;'
 
-run_sql 'SELECT count(1), sum(a) FROM partitioned.a;'
-check_contains 'count(1): 7'
-check_contains 'sum(a): 277151781'
+    run_lightning --backend $BACKEND
 
-run_sql "SHOW TABLE STATUS FROM partitioned WHERE name = 'a';"
-check_contains 'Create_options: partitioned'
+    run_sql 'SELECT count(1), sum(a) FROM partitioned.a;'
+    check_contains 'count(1): 8'
+    check_contains 'sum(a): 277151781'
+
+    run_sql "SHOW TABLE STATUS FROM partitioned WHERE name = 'a';"
+    check_contains 'Create_options: partitioned'
+done
diff --git a/tests/tiflash/run.sh b/tests/tiflash/run.sh
index 2102f5d73..74d4d094e 100644
--- a/tests/tiflash/run.sh
+++ b/tests/tiflash/run.sh
@@ -13,8 +13,8 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-# fi cluster version < v3.1.0 || $TIFLASH is not set, skip this test
-(check_cluster_version 3 1 0 'TiFlash' && [ -n "$TIFLASH" ]) || exit 0
+# before v4.0.5 tiflash doesn't support tls, so we should skip this test then
+(check_cluster_version 4 0 5 'TiFlash' && [ -n "$TIFLASH" ]) || exit 0
 
 set -euE
 # Populate the mydumper source